Non-inflationary theories of the genesis of the universe or what we know as the big bang effectively only discuss the hydrogen and helium particles etc &c., that fill the universe or what occurred after the birth of the universe, and now that evidence has been shown[1] that the universe is actually expanding, it has led to questions of what could have been prior to the bang in a much more sophisticated manner. And there are multiple theories, such as Brane collision or the collision of two dimensions or that the universe is formed from within a black hole, all of which are interesting particularly with new areas of thought viz., superstrings and the cyclic universe model, but certainly not as persuasive as cosmic inflation and the multiverse theory.

It is a theory that the universe is constantly expanding, while the density remains at a constant and during the process of decay, pockets of new universes form making our universe one of multiple universes in an eternal stretch of fields. The idea of the cosmological constant λ was formulated by Einstein in his theory of general relativity to describe a static universe prior to Hubble’ discovery that the universe was actually expanding and at the time he himself even rejected this equation, however it appears that the answer for cosmic inflation and the uniformity of the universe can unexpectedly be explained by it. How? According to Alan Guth it can be explained through repulsive gravity, namely that negative pressure can push exponential expansion far greater than its capacity for decay.

At this point where I found myself throwing whatever it was in my hand, cursing and walking briskly around the room for no apparent reason other than sheer excitement. How can zero build an eternally expanding universe? At elementary level, the underpinning of the cosmological constant is that gravity is not always attractive and can behave repulsively,[2] a necessary formulation to counter the problem with a static universe and the big crunch [collapse of the universe]; the negative pressure will provide the force that pushes things apart while the positive three-dimensional field will keep it together as they work in uniformity and subsequently expand. Whilst Einstein’ depiction of the universe may have been incorrect and why the theory was abandoned, the equations nevertheless remained functional with the laws of general relativity, hence its revival particularly within particle physics.

Gravitational repulsion requires a negative pressure, the latter along with energy density can produce cosmic gravitational fields.[3] In Newtonian physics, gravity is an attractive force and yet in the absence of pressure [pressure is a form of gravity] produces deceleration, even with gravitational fields having negative energy. As a comparative analogy, Coulomb’s inverse-square law in proportion to two charges divided by the square of the distance between them[4] (viz. gravity), the constant in the law is that the force between two positive charges is proportional to the product of their charges (like how two positive charges repel one another) and to calculate the energy density in an electrostatic field, more charge would induce more electric force that it no longer depends on the quantity of the charge, thus the two cancel each other out. In gravitational energy terms, not everything is positive and there are negative energies, with positive energy inflating or getting larger as long as there is an accompaniment of increasing quantity of negative energy, thus both offset each other and you have expansion locked at an exponential rate. In order for inflation to begin, a portion of this negative pressure is required for the existence of the early universe, namely that within the context of the grand unification theory – the merging of strong and weak nuclear forces along with gravitation and electromagnetism into a singular interaction – and the energy of the electromagnetic forces interact to form a unified energy value. This very portion of what becomes the big bang and the universe as we know it would be about the size of 10^-28cm (assuming energies being at 10^16 GeV – the problem of thermodynamic arrow relates to inhomogeneity[5] in that anything larger or smaller would make the universe blow apart or suck away galaxies into black holes, an important algorithm vis-à-vis temporal asymmetry where the time-dependence of Ω-1 changes, of which I will discuss later). It then grows at an exponential rate to build what we know as the universe and the mass density does not decrease, namely that it expands at a constant density. Where does the energy – that is constant per volume during growth – come from? As energy equals to positive matter and negative gravity, they cancel one another out in perfect harmony and thus the total energy levels for the universe can be measured at zero.

The universe has no energy? *Quizzical look

Acceleration? This is where the concept of ‘dark energy’ [what I call the ‘will’ of the universe] which makes up about ¾ of the universe comes to the fore or what is known as vacuum energy, considered to be empty [although in cosmology whilst the structure is fundamental to empty space nonetheless contains an energy density, namely the conservation of energy can occur at zero]. The total energy at the beginning of the universe must be at zero with the negative contribution to the energy of the cosmic gravitational field cancelling the energy of matter. Inflation as a constant and eternal is only possible at 0 where matter is being created by the inflation but controlled by the non-uniformity in perfect harmony. The repulsive gravity that drives inflation nevertheless decays [t=10^-33 seconds after the big bang] but the inflation itself remains eternal because the growth of the volume is faster – hence the importance of the thermodynamic arrow of time – than the metastable rate of the decay; the material formed during this process thus becomes the particles required to produce the very same material that forms another universe, ad infinitum (radiation density during this time redshifts away – again I will discuss later in addition to how dark energy appeases the early specialness issue by smoothening the inflationary transition). States of equilibrium can nonetheless be achieved in unstable, disordered environments, such as balancing a spinning basketball on an index finger where for a brief moment in time is in perfect equilibrium but certainly not at a stable one. Inflation is really the physics of scalar fields φ and matter; the particles that make up the universe that form the stuff following the initial phase of inflation leading to the big bang are merely the quantum representation of the (Higgs) fields. In particle physics, the nonzero Higgs field – which is responsible for the emergence of elementary particle masses – contains both positive and negative contributions and has a constant value at every space time point. Observable quantum density fluctuations and tensor perturbations in scalar fields can explain the source of temperature anisotropies (along with universal isotropy, its massive size and relative homogeneity) in the cosmic microwave background (CMB) radiation.[6] As the expansion of the universe is accelerating rather than slowing down under the influence of gravity, it indicates that vacuum energy is simply the energy of empty space and though empty has a mass density (which would mean that it is not actually empty).

Nevertheless, there are a plethora of issues raised at this point. The confusion or controversy really boils down to the concept of disorder and the cosmological epoch. Namely, is the universe a n-dimensional De Sitter space dSn, is it a 3-manifold Poincaré dodecahedral space, the flatness problem where Euclidian geometry applies only at a large scale; is it three-dimensional, four-dimensional, or nine-dimensional squished into three as string theorists propose? The other and perhaps more interesting one is the problem of entropy potentially being extremely low at this point. Whilst warm inflation – modelled on the standard or ‘cold’ inflationary theory[7] – purports a small portion of the vacuum energy density is converted to radiation, whereby the radiation density stabilises during the process of coupling [between inflation and radiation fields], during the decay phase, the scalar field oscillates to become radiation particles that slowly reheats the universe and when this occurs [reheating and inflation together] they become coupled into a unified process. The connection between the flatness problem and entropy is a complex one, particularly related to whether the early universe was adiabatic and why spatially the conditions at the beginning were flat. When inflation begins, the energy stored in the gravitational field as it expands increases whilst the energy density remains constant, thus the gravitational field itself has a repulsive energy density as it expands in volume, with the total energy being very close to 0 without violating the conservation of energy. It may mean that inflation requires a non-adiabatic, extremely low entropy to occur, entropy being the measure of randomness and low entropy itself considered perfectly ordered. If inflation increases entropy, it appears that at the point of inflation, the entropy had to be smaller and the uniformity of the energy density during inflation becomes responsible for the low entropy conditions. What is currently in debate is namely why – in the past – did the universe begin with low entropy and yet the product being the second law of thermodynamics?

I want to maintain that the observable universe (and one should note the keyword here being ‘observable’) would imply that the universe is flat (k=0) or that inflation is pushing Ω to 1 with Ω being the mass density divided by critical mass density, thus the asymptotic curvature of the universe is being exponentially flattened by the expansion at 10^35 seconds after the bang. What that means is that should Ω=1 the curvature must equal to 0 (or be extremely close to it) and the effect would be infinite expansion. Thinking about that model, such expansion could causally be the precise reason we have an arrow of time fixed in perfect and irremediable harmony, although no theory of randomness can explain the arrow of time and the problem of low entropy during the early phase of the universe and the successive phase transition of expansion and cooling. When assessing temporal asymmetry, however, the concept of low entropy during the beginning phases of the universe – whilst objectionable or perhaps superfluous – is nevertheless useful when ascertaining the thermodynamic arrow.

The second law of thermodynamics purports that the time flows in a linear direction as we know it, namely from past to present to future. The question here is that as the universe expands and progresses over this time, from an ordered state – namely that of low-entropy – it is moving toward a high-entropy disordered universe. Entanglement in ordinary quantum mechanics, which can perhaps work as a correlation in that the measurements of the relationship between two particles relies on contact sometime in the past, the interaction or exchange following even when these particles are at a far distance and in a disordered state from one another remain organised and can even affect one another’ quantum state. As a consequence, while separate their properties can only be measured as one. There is an invisible but an active link between the particles. In quantum field theory, entanglement entropy rather than being a correlation contains causality under the assumption that symmetry of a pure state that has ergodic properties.

The total energy at the beginning of the universe started at very close to zero and the negative contribution to the energy of the gravitational field cancels the energy of matter and thus repulsive gravity drives inflation with the growth volume faster than the decay, allowing the physical universe to expand exponentially. We are able to confirm relative homogeneity and isotropy through the fluctuations imprinted in the anisotropy of the cosmic microwave background and gives light to the conditions of the early universe, which was once filled with plasma but where photons themselves – whilst moving at the speed of light – remained immobile in the density and so velocity stood at zero. As the universe expanded, the plasma cooled and became a gas and as such cosmologists began to question thermal equilibrium, the second law of thermodynamics and entropy, the latter allegedly being low during the early epoch of the universe. Thus in continuation, the problem we face here is that as the universe expands and progresses over this time, from an ordered state – namely that of low-entropy – toward a disordered high-entropy, the latter itself dependent on the arrow of time, how exactly can the early universe in the past, where it was hotter and denser and had a stronger gravitation pull, be perfectly smooth?

Hubble expansion, which is about 70km per megaparsec, is the expansion rate that we see at present with the inflationary epoch ending 10^-32 seconds after the big bang to expand at the rate of the Hubble constant.[8] If the universe was thus once condensed to a very small size until it expanded at a factor of 10^26 due to inflation and eventually ending that lead to a fixed or steady expansion as we know is now taking place, the process itself nevertheless preserves the subatomic smoothness that the initial conditions held. This is particularly coherent when assuming that we are a part of a multiverse. In Einstein’ GR field equations, he applied the cosmological constant Λ in an attempt to explain a static universe prior to Hubble’ expanding one and thus later rejected it, however for both inflation and dark energy, the ubiquitous Λ becomes a necessary algorithm that binds the theory together as the energy density of the latter in particular causally drives expansion and a flat universe that can expand infinitely. With Riemannian geometry, cosmological observations of the CMB radiation through the Wilkinson Microwave Anisotropy Probe (WMAP) have measured angles that add to exactly 180 degrees, which in a Euclidean space purports a universe that is k=0 or flat[9] and as its density remains constant as it expands, dark energy or the energy of empty space itself plays a vital role. The horizon problem also shows that the temperatures at different directions of the CMB radiation are uniform to almost 1 part in 10^4 [accounting a minor electric dipole] or 1 part in 10,000 and therefore almost the same – something that should not actually be possible – purporting that the only solution to this thermal equilibrium is inflation. That is, for example, regions billions of light years in opposite directions must communicate or interact in some manner to reach this symmetry and the explanation is that they – at one point in time – were interacting and the process of inflation has stretched them out into altered directions, thus favouring the model of an isotropic and homogenous universe.

As there is an arrow of time and as the universe is expanding, in the past the universe would have been infinitesimally smaller particularly as we reach the beginning of time. As such, the density and heat would have been higher – something clearly attributable to the CMB radiation – and the fact that perfection or a state of low-entropy is requisite should we adhere to thermodynamic laws and the direction of time, the conditions of the big bang becomes formidable. In addition, if the initial conditions were not perfectly ordered and smooth, it would have fizzled away. As mentioned, assuming the universe is geometrically flat because of the ratio between the mass density and the critical mass density being very close to Ω =1 and stabilised through the force of repulsive gravity as illustrated by the cosmological constant, is the fabric of the universe smoothing as it expands. I will write more about the Arrow of Time and Thermodynamics in my next post.

##### [1] Stephen T. Thornton and Andrew Rex, Modern Physics for Scientists and Engineers, Cengage Learning (2012) 578

[2] Behram N. Kursunogammalu, Stephan L. Mintz, Arnold Perlmutter, The Role of Neutrinos, Strings, Gravity, and Variable Cosmological Constant in Elementary Particle Physics, Springer Science & Business Media (2007) 182

[3] Maurizio Gasperini, The Universe Before the Big Bang: Cosmology and String Theory, 160

[4] John Gribbin, Mary Gribbin, Jonathan Gribbin, Q is for Quantum: An Encyclopedia of Particle Physics, Simon and Schuster (2000) 92

[5] Murray Gell-Mann and James B. Hartle, Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology, (February, 2008)

[6] Alejandro Gangui, Cosmic Microwave Background Anisotropies and Theories of the Early Universe, SISSA-International School for Advanced Studies (1995)

[7] Mar Bastero-Gil, Arjun Berera, Ian G. Moss, Rudnei O. Ramos, Theory of non-Gaussianity in warm inflation (Dec 2014)

[8] Cesare Emiliani, Planet Earth: Cosmology, Geology, and the Evolution of Life and Environment, Cambridge University Press (1992) 68

[9] Carlos I. Calle, Einstein For Dummies, Wiley (2005) 309

[10] Don S. Lemons, A Student’s Guide to Entropy, Cambridge University Press (2013) 72

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Non-inflationary theories of the genesis of the universe or what we know as the big bang effectively only discuss the hydrogen and helium particles etc &c., that fill the universe or what occurred after the birth of the universe, and now that evidence has been shown[1] that the universe is actually expanding, it has led to questions of what could have been prior to the bang in a much more sophisticated manner. And there are multiple theories, such as Brane collision or the collision of two dimensions or that the universe is formed from within a black hole, all of which are interesting particularly with new areas of thought viz., superstrings and the cyclic universe model, but certainly not as persuasive as cosmic inflation and the multiverse theory.

It is a theory that the universe is constantly expanding, while the density remains at a constant and during the process of decay, pockets of new universes form making our universe one of multiple universes in an eternal stretch of fields. The idea of the cosmological constant λ was formulated by Einstein in his theory of general relativity to describe a static universe prior to Hubble’ discovery that the universe was actually expanding and at the time he himself even rejected this equation, however it appears that the answer for cosmic inflation and the uniformity of the universe can unexpectedly be explained by it. How? According to Alan Guth it can be explained through repulsive gravity, namely that negative pressure can push exponential expansion far greater than its capacity for decay.

At this point where I found myself throwing whatever it was in my hand, cursing and walking briskly around the room for no apparent reason other than sheer excitement. How can zero build an eternally expanding universe? At elementary level, the underpinning of the cosmological constant is that gravity is not always attractive and can behave repulsively,[2] a necessary formulation to counter the problem with a static universe and the big crunch [collapse of the universe]; the negative pressure will provide the force that pushes things apart while the positive three-dimensional field will keep it together as they work in uniformity and subsequently expand. Whilst Einstein’ depiction of the universe may have been incorrect and why the theory was abandoned, the equations nevertheless remained functional with the laws of general relativity, hence its revival particularly within particle physics.

Gravitational repulsion requires a negative pressure, the latter along with energy density can produce cosmic gravitational fields.[3] In Newtonian physics, gravity is an attractive force and yet in the absence of pressure [pressure is a form of gravity] produces deceleration, even with gravitational fields having negative energy. As a comparative analogy, Coulomb’s inverse-square law in proportion to two charges divided by the square of the distance between them[4] (viz. gravity), the constant in the law is that the force between two positive charges is proportional to the product of their charges (like how two positive charges repel one another) and to calculate the energy density in an electrostatic field, more charge would induce more electric force that it no longer depends on the quantity of the charge, thus the two cancel each other out. In gravitational energy terms, not everything is positive and there are negative energies, with positive energy inflating or getting larger as long as there is an accompaniment of increasing quantity of negative energy, thus both offset each other and you have expansion locked at an exponential rate. In order for inflation to begin, a portion of this negative pressure is required for the existence of the early universe, namely that within the context of the grand unification theory – the merging of strong and weak nuclear forces along with gravitation and electromagnetism into a singular interaction – and the energy of the electromagnetic forces interact to form a unified energy value. This very portion of what becomes the big bang and the universe as we know it would be about the size of 10^-28cm (assuming energies being at 10^16 GeV – the problem of thermodynamic arrow relates to inhomogeneity[5] in that anything larger or smaller would make the universe blow apart or suck away galaxies into black holes, an important algorithm vis-à-vis temporal asymmetry where the time-dependence of Ω-1 changes, of which I will discuss later). It then grows at an exponential rate to build what we know as the universe and the mass density does not decrease, namely that it expands at a constant density. Where does the energy – that is constant per volume during growth – come from? As energy equals to positive matter and negative gravity, they cancel one another out in perfect harmony and thus the total energy levels for the universe can be measured at zero.

The universe has no energy? *Quizzical look

Acceleration? This is where the concept of ‘dark energy’ [what I call the ‘will’ of the universe] which makes up about ¾ of the universe comes to the fore or what is known as vacuum energy, considered to be empty [although in cosmology whilst the structure is fundamental to empty space nonetheless contains an energy density, namely the conservation of energy can occur at zero]. The total energy at the beginning of the universe must be at zero with the negative contribution to the energy of the cosmic gravitational field cancelling the energy of matter. Inflation as a constant and eternal is only possible at 0 where matter is being created by the inflation but controlled by the non-uniformity in perfect harmony. The repulsive gravity that drives inflation nevertheless decays [t=10^-33 seconds after the big bang] but the inflation itself remains eternal because the growth of the volume is faster – hence the importance of the thermodynamic arrow of time – than the metastable rate of the decay; the material formed during this process thus becomes the particles required to produce the very same material that forms another universe, ad infinitum (radiation density during this time redshifts away – again I will discuss later in addition to how dark energy appeases the early specialness issue by smoothening the inflationary transition). States of equilibrium can nonetheless be achieved in unstable, disordered environments, such as balancing a spinning basketball on an index finger where for a brief moment in time is in perfect equilibrium but certainly not at a stable one. Inflation is really the physics of scalar fields φ and matter; the particles that make up the universe that form the stuff following the initial phase of inflation leading to the big bang are merely the quantum representation of the (Higgs) fields. In particle physics, the nonzero Higgs field – which is responsible for the emergence of elementary particle masses – contains both positive and negative contributions and has a constant value at every space time point. Observable quantum density fluctuations and tensor perturbations in scalar fields can explain the source of temperature anisotropies (along with universal isotropy, its massive size and relative homogeneity) in the cosmic microwave background (CMB) radiation.[6] As the expansion of the universe is accelerating rather than slowing down under the influence of gravity, it indicates that vacuum energy is simply the energy of empty space and though empty has a mass density (which would mean that it is not actually empty).

Nevertheless, there are a plethora of issues raised at this point. The confusion or controversy really boils down to the concept of disorder and the cosmological epoch. Namely, is the universe a n-dimensional De Sitter space dSn, is it a 3-manifold Poincaré dodecahedral space, the flatness problem where Euclidian geometry applies only at a large scale; is it three-dimensional, four-dimensional, or nine-dimensional squished into three as string theorists propose? The other and perhaps more interesting one is the problem of entropy potentially being extremely low at this point. Whilst warm inflation – modelled on the standard or ‘cold’ inflationary theory[7] – purports a small portion of the vacuum energy density is converted to radiation, whereby the radiation density stabilises during the process of coupling [between inflation and radiation fields], during the decay phase, the scalar field oscillates to become radiation particles that slowly reheats the universe and when this occurs [reheating and inflation together] they become coupled into a unified process. The connection between the flatness problem and entropy is a complex one, particularly related to whether the early universe was adiabatic and why spatially the conditions at the beginning were flat. When inflation begins, the energy stored in the gravitational field as it expands increases whilst the energy density remains constant, thus the gravitational field itself has a repulsive energy density as it expands in volume, with the total energy being very close to 0 without violating the conservation of energy. It may mean that inflation requires a non-adiabatic, extremely low entropy to occur, entropy being the measure of randomness and low entropy itself considered perfectly ordered. If inflation increases entropy, it appears that at the point of inflation, the entropy had to be smaller and the uniformity of the energy density during inflation becomes responsible for the low entropy conditions. What is currently in debate is namely why – in the past – did the universe begin with low entropy and yet the product being the second law of thermodynamics?

I want to maintain that the observable universe (and one should note the keyword here being ‘observable’) would imply that the universe is flat (k=0) or that inflation is pushing Ω to 1 with Ω being the mass density divided by critical mass density, thus the asymptotic curvature of the universe is being exponentially flattened by the expansion at 10^35 seconds after the bang. What that means is that should Ω=1 the curvature must equal to 0 (or be extremely close to it) and the effect would be infinite expansion. Thinking about that model, such expansion could causally be the precise reason we have an arrow of time fixed in perfect and irremediable harmony, although no theory of randomness can explain the arrow of time and the problem of low entropy during the early phase of the universe and the successive phase transition of expansion and cooling. When assessing temporal asymmetry, however, the concept of low entropy during the beginning phases of the universe – whilst objectionable or perhaps superfluous – is nevertheless useful when ascertaining the thermodynamic arrow.

The second law of thermodynamics purports that the time flows in a linear direction as we know it, namely from past to present to future. The question here is that as the universe expands and progresses over this time, from an ordered state – namely that of low-entropy – it is moving toward a high-entropy disordered universe. Entanglement in ordinary quantum mechanics, which can perhaps work as a correlation in that the measurements of the relationship between two particles relies on contact sometime in the past, the interaction or exchange following even when these particles are at a far distance and in a disordered state from one another remain organised and can even affect one another’ quantum state. As a consequence, while separate their properties can only be measured as one. There is an invisible but an active link between the particles. In quantum field theory, entanglement entropy rather than being a correlation contains causality under the assumption that symmetry of a pure state that has ergodic properties.

The total energy at the beginning of the universe started at very close to zero and the negative contribution to the energy of the gravitational field cancels the energy of matter and thus repulsive gravity drives inflation with the growth volume faster than the decay, allowing the physical universe to expand exponentially. We are able to confirm relative homogeneity and isotropy through the fluctuations imprinted in the anisotropy of the cosmic microwave background and gives light to the conditions of the early universe, which was once filled with plasma but where photons themselves – whilst moving at the speed of light – remained immobile in the density and so velocity stood at zero. As the universe expanded, the plasma cooled and became a gas and as such cosmologists began to question thermal equilibrium, the second law of thermodynamics and entropy, the latter allegedly being low during the early epoch of the universe. Thus in continuation, the problem we face here is that as the universe expands and progresses over this time, from an ordered state – namely that of low-entropy – toward a disordered high-entropy, the latter itself dependent on the arrow of time, how exactly can the early universe in the past, where it was hotter and denser and had a stronger gravitation pull, be perfectly smooth?

Hubble expansion, which is about 70km per megaparsec, is the expansion rate that we see at present with the inflationary epoch ending 10^-32 seconds after the big bang to expand at the rate of the Hubble constant.[8] If the universe was thus once condensed to a very small size until it expanded at a factor of 10^26 due to inflation and eventually ending that lead to a fixed or steady expansion as we know is now taking place, the process itself nevertheless preserves the subatomic smoothness that the initial conditions held. This is particularly coherent when assuming that we are a part of a multiverse. In Einstein’ GR field equations, he applied the cosmological constant Λ in an attempt to explain a static universe prior to Hubble’ expanding one and thus later rejected it, however for both inflation and dark energy, the ubiquitous Λ becomes a necessary algorithm that binds the theory together as the energy density of the latter in particular causally drives expansion and a flat universe that can expand infinitely. With Riemannian geometry, cosmological observations of the CMB radiation through the Wilkinson Microwave Anisotropy Probe (WMAP) have measured angles that add to exactly 180 degrees, which in a Euclidean space purports a universe that is k=0 or flat[9] and as its density remains constant as it expands, dark energy or the energy of empty space itself plays a vital role. The horizon problem also shows that the temperatures at different directions of the CMB radiation are uniform to almost 1 part in 10^4 [accounting a minor electric dipole] or 1 part in 10,000 and therefore almost the same – something that should not actually be possible – purporting that the only solution to this thermal equilibrium is inflation. That is, for example, regions billions of light years in opposite directions must communicate or interact in some manner to reach this symmetry and the explanation is that they – at one point in time – were interacting and the process of inflation has stretched them out into altered directions, thus favouring the model of an isotropic and homogenous universe.

As there is an arrow of time and as the universe is expanding, in the past the universe would have been infinitesimally smaller particularly as we reach the beginning of time. As such, the density and heat would have been higher – something clearly attributable to the CMB radiation – and the fact that perfection or a state of low-entropy is requisite should we adhere to thermodynamic laws and the direction of time, the conditions of the big bang becomes formidable. In addition, if the initial conditions were not perfectly ordered and smooth, it would have fizzled away. As mentioned, assuming the universe is geometrically flat because of the ratio between the mass density and the critical mass density being very close to Ω =1 and stabilised through the force of repulsive gravity as illustrated by the cosmological constant, is the fabric of the universe smoothing as it expands. I will write more about the Arrow of Time and Thermodynamics in my next post.

## [1] Stephen T. Thornton and Andrew Rex, Modern Physics for Scientists and Engineers, Cengage Learning (2012) 578

[2] Behram N. Kursunogammalu, Stephan L. Mintz, Arnold Perlmutter, The Role of Neutrinos, Strings, Gravity, and Variable Cosmological Constant in Elementary Particle Physics, Springer Science & Business Media (2007) 182

[3] Maurizio Gasperini, The Universe Before the Big Bang: Cosmology and String Theory, 160

[4] John Gribbin, Mary Gribbin, Jonathan Gribbin, Q is for Quantum: An Encyclopedia of Particle Physics, Simon and Schuster (2000) 92

[5] Murray Gell-Mann and James B. Hartle, Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology, (February, 2008)

[6] Alejandro Gangui, Cosmic Microwave Background Anisotropies and Theories of the Early Universe, SISSA-International School for Advanced Studies (1995)

[7] Mar Bastero-Gil, Arjun Berera, Ian G. Moss, Rudnei O. Ramos, Theory of non-Gaussianity in warm inflation (Dec 2014)

[8] Cesare Emiliani, Planet Earth: Cosmology, Geology, and the Evolution of Life and Environment, Cambridge University Press (1992) 68

[9] Carlos I. Calle, Einstein For Dummies, Wiley (2005) 309

[10] Don S. Lemons, A Student’s Guide to Entropy, Cambridge University Press (2013) 72

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