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Cyclic universe from uniform rate inflation on the brane with a timelike extra dimension

Rikpratik Sengupta, Arkajit Aich, Kaushik Bhattacharya

TL;DR

The paper addresses the challenge of the Big Bang singularity by embedding a non-singular cyclic cosmology within a timelike Shtanov–Sahni brane, where uniform-rate inflation coexists with anisotropy modeled by a secondary scalar field. It derives analytic background solutions for two cases of shear dynamics (Cases 1 and 2) under a constant inflaton roll rate $\dot{\phi}=-\lambda$ and analyzes primordial perturbations using the $\delta N$ formalism. Perturbation predictions ($n_s \approx 0.9659$, $r \approx 10^{-6}$) are compatible with Planck data for realistic parameter choices, even with sizable initial anisotropy, thanks to high-energy brane corrections that suppress shear near the bounce. The results show that a timelike extra dimension can robustly unify non-singular early-universe dynamics with precision cosmology, offering a compelling alternative to standard inflation.

Abstract

We investigate a non-singular cosmological scenario in which uniform-rate inflation is realised on an anisotropic Shtanov-Sahni braneworld. The model naturally resolves the initial singularity resulting in an infinite number of smooth non-singular bounces, while accommodating a phase of accelerated expansion driven by a scalar field rolling at a constant rate. The presence of a timelike extra dimension induces high-energy corrections to the effective Friedmann dynamics, allowing anisotropic shear to be dynamically suppressed near the bounce and rendering the background evolution stable. We derive the full background dynamics analytically and demonstrate that uniform-rate inflation can be consistently embedded within an anisotropic braneworld framework. Primordial scalar and tensor perturbations are analysed using the $δN$ formalism, ensuring that only physically relevant modes exiting the horizon during inflation contribute to observable quantities. Remarkably, we find that observational consistency can be achieved with different levels of anisotropy in the two different scenarios we consider, without compromising the smoothness or stability of the bounce. Our results establish uniform-rate inflation on an anisotropic braneworld as a robust and observationally viable alternative to standard inflationary cosmology, offering a compelling framework in which non-singular early-universe dynamics and precision cosmology can be consistently unified.

Cyclic universe from uniform rate inflation on the brane with a timelike extra dimension

TL;DR

The paper addresses the challenge of the Big Bang singularity by embedding a non-singular cyclic cosmology within a timelike Shtanov–Sahni brane, where uniform-rate inflation coexists with anisotropy modeled by a secondary scalar field. It derives analytic background solutions for two cases of shear dynamics (Cases 1 and 2) under a constant inflaton roll rate and analyzes primordial perturbations using the formalism. Perturbation predictions (, ) are compatible with Planck data for realistic parameter choices, even with sizable initial anisotropy, thanks to high-energy brane corrections that suppress shear near the bounce. The results show that a timelike extra dimension can robustly unify non-singular early-universe dynamics with precision cosmology, offering a compelling alternative to standard inflation.

Abstract

We investigate a non-singular cosmological scenario in which uniform-rate inflation is realised on an anisotropic Shtanov-Sahni braneworld. The model naturally resolves the initial singularity resulting in an infinite number of smooth non-singular bounces, while accommodating a phase of accelerated expansion driven by a scalar field rolling at a constant rate. The presence of a timelike extra dimension induces high-energy corrections to the effective Friedmann dynamics, allowing anisotropic shear to be dynamically suppressed near the bounce and rendering the background evolution stable. We derive the full background dynamics analytically and demonstrate that uniform-rate inflation can be consistently embedded within an anisotropic braneworld framework. Primordial scalar and tensor perturbations are analysed using the formalism, ensuring that only physically relevant modes exiting the horizon during inflation contribute to observable quantities. Remarkably, we find that observational consistency can be achieved with different levels of anisotropy in the two different scenarios we consider, without compromising the smoothness or stability of the bounce. Our results establish uniform-rate inflation on an anisotropic braneworld as a robust and observationally viable alternative to standard inflationary cosmology, offering a compelling framework in which non-singular early-universe dynamics and precision cosmology can be consistently unified.
Paper Structure (5 sections, 89 equations, 10 figures)

This paper contains 5 sections, 89 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Mathematical formulation of the model
  3. Case 1 : $\dot\phi_a^2 = \Sigma(\Sigma - \frac{V(\phi)}{\lambda})$
  4. Case 2: $\dot\phi_a^2 = 2\frac{\Sigma}{\lambda}(e^{\frac{\Sigma}{\lambda}}-1)V(\phi)$
  5. Conclusion

Figures (10)

  • Figure 1: Variation of the inflation potential $V(\phi)$ vs the inflaton field $\phi$.
  • Figure 2: Variation of anisotropy field $\phi_a$ with cosmic time $t$.
  • Figure 3: Variation of total energy density with cosmic time.
  • Figure 4: Variation of the Hubble parameter $H$ with cosmic time $t$.
  • Figure 5: Variation of the scale factor with cosmic time $t$.
  • ...and 5 more figures