# A simple model of universe describing the early inflation and the late accelerated expansion in a symmetric manner

## Abstract

We construct a simple model of universe which 'unifies' vacuum energy and radiation on the one hand, and matter and dark energy on the other hand in the spirit of a generalized Chaplygin gas model. Specifically, the phases of early inflation and late accelerated expansion are described by a generalized equation of state p/c{sup 2} = αρ+kρ{sup 1+1/n} having a linear component p = αρc{sup 2} and a polytropic component p = kρ{sup 1+1/n}c{sup 2}. For α= 1/3, n= 1 and k=−4/(3ρ{sub P}), where ρ{sub P}= 5.1610{sup 99} g/m{sup 3} is the Planck density, this equation of state describes the transition between the vacuum energy era and the radiation era. For t≥ 0, the universe undergoes an inflationary expansion that brings it from the Planck size l{sub P}= 1.6210{sup −35} m to a size a{sub 1}= 2.6110{sup −6} m on a timescale of about 23.3 Planck times t{sub P}= 5.3910{sup −44} s (early inflation). When t > t{sub 1}= 23.3t{sub P}, the universe decelerates and enters in the radiation era. We interpret the transition from the vacuum energy era to the radiation era as a second order phase transition where the Planck constant ℏ plays the role of finite sizemore »

- Authors:

- Laboratoire de Physique Théorique (IRSAMC), CNRS and UPS, Université de Toulouse (France)

- Publication Date:

- OSTI Identifier:
- 22218296

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1548; Journal Issue: 1; Conference: 9. Mexican school on gravitation and mathematical physics: Cosmology for the 21. century, Puerto Vallarta, Jalisco (Mexico), 3-7 Dec 2012; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACCELERATION; ASTROPHYSICS; BARYONS; COSMOLOGICAL CONSTANT; COSMOLOGY; DENSITY; EQUATIONS OF STATE; FUNDAMENTAL CONSTANTS; INFLATIONARY UNIVERSE; NONLUMINOUS MATTER; PHASE TRANSFORMATIONS; SCALAR FIELDS; SYMMETRY; TACHYONS; UNIVERSE

### Citation Formats

```
Chavanis, Pierre-Henri.
```*A simple model of universe describing the early inflation and the late accelerated expansion in a symmetric manner*. United States: N. p., 2013.
Web. doi:10.1063/1.4817032.

```
Chavanis, Pierre-Henri.
```*A simple model of universe describing the early inflation and the late accelerated expansion in a symmetric manner*. United States. doi:10.1063/1.4817032.

```
Chavanis, Pierre-Henri. Tue .
"A simple model of universe describing the early inflation and the late accelerated expansion in a symmetric manner". United States. doi:10.1063/1.4817032.
```

```
@article{osti_22218296,
```

title = {A simple model of universe describing the early inflation and the late accelerated expansion in a symmetric manner},

author = {Chavanis, Pierre-Henri},

abstractNote = {We construct a simple model of universe which 'unifies' vacuum energy and radiation on the one hand, and matter and dark energy on the other hand in the spirit of a generalized Chaplygin gas model. Specifically, the phases of early inflation and late accelerated expansion are described by a generalized equation of state p/c{sup 2} = αρ+kρ{sup 1+1/n} having a linear component p = αρc{sup 2} and a polytropic component p = kρ{sup 1+1/n}c{sup 2}. For α= 1/3, n= 1 and k=−4/(3ρ{sub P}), where ρ{sub P}= 5.1610{sup 99} g/m{sup 3} is the Planck density, this equation of state describes the transition between the vacuum energy era and the radiation era. For t≥ 0, the universe undergoes an inflationary expansion that brings it from the Planck size l{sub P}= 1.6210{sup −35} m to a size a{sub 1}= 2.6110{sup −6} m on a timescale of about 23.3 Planck times t{sub P}= 5.3910{sup −44} s (early inflation). When t > t{sub 1}= 23.3t{sub P}, the universe decelerates and enters in the radiation era. We interpret the transition from the vacuum energy era to the radiation era as a second order phase transition where the Planck constant ℏ plays the role of finite size effects (the standard Big Bang theory is recovered for ℏ= 0). For α= 0, n=−1 and k=−ρ{sub Λ}, where ρ{sub Λ}= 7.0210{sup −24} g/m{sup 3} is the cosmological density, the equation of state p/c{sup 2} = αρ+kρ{sup 1+1/n} describes the transition from a decelerating universe dominated by pressureless matter (baryonic and dark matter) to an accelerating universe dominated by dark energy (late inflation). This transition takes place at a size a{sub 2}= 0.204l{sub Λ}. corresponding to a time t{sub 2}= 0.203t{sub Λ} where l{sub Λ}= 4.38 10{sup 26} m is the cosmological length and t{sub Λ}= 1.46 10{sup 18} s the cosmological time. The present universe turns out to be just at the transition between these two periods (t{sub 0}∼t{sub 2}). Our model gives the same results as the standard ΛCDM model for t≫t{sub P} and completes it by incorporating a phase of early inflation for t < 23.3t{sub P} in a very natural manner. Furthermore, it reveals a nice 'symmetry' between the early and the late evolution of the universe. The early universe is modeled by a polytrope n=+ 1 and the late universe by a polytrope n=−1. Furthermore, the cosmological constant Λ in the late universe plays a role similar to the Planck constant ℏ in the early universe. The mathematical formulae in the early and in the late universe are then strikingly symmetric. We interpret the cosmological constant as a fundamental constant of Nature describing the 'cosmophysics' just like the Planck constant describes the 'microphysics'. The Planck density and the cosmological density represent fundamental upper and lower bounds differing by 122 orders of magnitude. The cosmological constant 'problem' may be a false problem. Finally, we show that our model admits a scalar field interpretation based on a quintessence field or a tachyon field.},

doi = {10.1063/1.4817032},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1548,

place = {United States},

year = {2013},

month = {7}

}