[Paper Review] GCG Inflation in the light of Planck and BICEP2

Bikas R Dinda, S. Kumar+1 more|arXiv (Cornell University)|Apr 14, 2014

Cosmology and Gravitation Theories15 references3 citations

TL;DR

This paper investigates Generalized Chaplygin Gas (GCG) as a viable inflationary model in a 5D brane world scenario, showing it can produce observable primordial fluctuations consistent with Planck and BICEP2 data. While GCG fails as an inflationary driver in 4D Einstein gravity, it succeeds in higher-dimensional cosmology, though it cannot resolve the BICEP2-Planck tension without a phantom dark energy equation of state.

ABSTRACT

In this work, we study an inflationary scenario in the presence of Generalized Chaplygin Gas (GCG). We show that in Einstein gravity, GCG is not a suitable candidate for inflation; but in a five dimensional brane world scenario, it can work as a viable inflationary model. We calculate the relevant quantities such as $n_{s}$, $r$ and $A_{s}$ related to the primordial scalar and tensor fluctuations, and using their recent bounds from Planck and BICEP2, we constrain the model parameters as well as the five-dimensional Planck mass. But as a slow-roll inflationary model with a power-law type scalar primordial power spectrum, GCG as an inflationary model can not resolve the tension between results from BICEP2 and Planck with a concordance $\Lambda$CDM universe. We show that with a phantom type dark energy equation of state, this tension may be eased.

Motivation & Objective

• To assess the viability of Generalized Chaplygin Gas (GCG) as an inflationary model in Einstein gravity and higher-dimensional brane world scenarios.
• To calculate key inflationary observables: scalar spectral index $n_s$, tensor-to-scalar ratio $r$, and amplitude $A_s$.
• To constrain model parameters and the 5D Planck mass using recent observational bounds from Planck and BICEP2.
• To investigate whether GCG inflation can alleviate the tension between BICEP2 and Planck results in the context of the $Λ$CDM model.
• To explore whether a phantom-type dark energy equation of state can ease the observed discrepancy in cosmological data.

Proposed method

• Formulate a 5D brane world cosmological model with GCG as the inflaton field.
• Derive the effective 4D Friedmann equation on the brane to describe scalar and tensor perturbations during inflation.
• Compute the primordial power spectra for scalar and tensor fluctuations using slow-roll approximation.
• Extract observables $n_s$, $r$, and $A_s$ from the power spectra and compare them with Planck and BICEP2 constraints.
• Perform parameter space scans to constrain the GCG parameters and the 5D Planck mass.
• Introduce a phantom-type dark energy equation of state to assess its impact on resolving the BICEP2-Planck tension.

Experimental results

Research questions

• RQ1 Can Generalized Chaplygin Gas serve as a viable inflaton in 4D Einstein gravity?
• RQ2 Does the 5D brane world scenario enable GCG to produce inflationary predictions consistent with Planck and BICEP2 data?
• RQ3 To what extent can the GCG model constrain the 5D Planck mass and other model parameters?
• RQ4 Can the GCG model resolve the discrepancy between BICEP2 and Planck observations in the $Λ$CDM framework?
• RQ5 Does introducing a phantom equation of state for dark energy reduce the tension between BICEP2 and Planck results?

Key findings

• In 4D Einstein gravity, GCG cannot serve as a viable inflationary model due to incompatible predictions for $n_s$ and $r$.
• In a 5D brane world scenario, GCG can produce inflationary dynamics consistent with Planck and BICEP2 constraints on $n_s$, $r$, and $A_s$.
• The model allows for constraints on the 5D Planck mass and GCG parameters through comparison with observational data.
• Despite fitting observational data, the GCG model with a power-law scalar power spectrum fails to resolve the tension between BICEP2 and Planck results in the $Λ$CDM framework.
• The inclusion of a phantom-type dark energy equation of state may ease the observed tension between BICEP2 and Planck data.