[Paper Review] Evidences for bouncing evolution before inflation in cosmological surveys

Jie Liu, Yi-Fu Cai+1 more|arXiv (Cornell University)|Sep 17, 2010

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes a phenomenological parametrization of the primordial power spectrum with a jump feature arising from a nonsingular bounce preceding inflation, using cosmological data (CMB, LSS, SNIa) to constrain bounce parameters via Markov Chain Monte Carlo (MCMC) global fitting. The key result is strong upper limits on bounce scale and duration, suggesting a fast, high-energy bounce scenario consistent with current observations.

ABSTRACT

Inflationary cosmology with a preceding nonsingular bounce can lead to changes on the primordial density fluctuations. One significant prediction is that the amplitude of the power spectrum may undergo a jump at a critical scale. In this Letter we propose a phenomenological parametrization of the primordial power spectrum in this scenario and confront the jump feature with latest cosmological data. Performing a global fitting, we utilize this possibility to derive a novel method for constraining bounce parameters via cosmological measurements. Combining the CMB, LSS and SNIa data, our result interestingly reveals that a nonsingular bounce, if exists, should be a fast bounce which happens at a very high energy scale, as we get an upper limit on the bounce parameters.

Motivation & Objective

• To investigate observational signatures of a nonsingular bounce preceding inflation in cosmological data.
• To develop a phenomenological parametrization of the primordial power spectrum that includes a jump feature due to bounce-induced amplitude changes.
• To constrain bounce parameters (scale and duration) using global fitting of CMB, large-scale structure, and Type Ia supernova data.
• To assess whether bounce inflation provides a better fit to current cosmological data than the standard ΛCDM model.

Proposed method

• A phenomenological parametrization of the primordial power spectrum is introduced, incorporating a jump at a critical scale k_B, characterized by amplitude T and scale k_B.
• The model assumes a matter-dominated contraction phase followed by a nonsingular bounce and subsequent inflation, leading to different perturbation amplitudes before and after the bounce.
• Markov Chain Monte Carlo (MCMC) techniques are employed to perform a global fitting of the model to combined CMB, LSS, and SNIa datasets.
• The likelihood is computed using WMAP, SDSS LRG, and SNLS Union data, with marginalization over nuisance parameters and inclusion of HST H₀ prior.
• χ² statistics are used to quantify goodness-of-fit, comparing the bounce model to ΛCDM and deriving constraints on bounce parameters.
• Contour plots are generated for H and Δt_B (inflationary Hubble scale and bounce duration) at 1σ and 2σ confidence levels.

Experimental results

Research questions

• RQ1 Can observational data constrain the existence and properties of a nonsingular bounce preceding inflation?
• RQ2 Does a jump feature in the primordial power spectrum provide a detectable signature in current cosmological data?
• RQ3 How do bounce parameters (k_B, T) affect the fit to CMB, LSS, and SNIa observations?
• RQ4 Is the bounce inflation model a better fit to data than the standard ΛCDM model?
• RQ5 What are the upper limits on the bounce scale and duration consistent with current observations?

Key findings

• The current data yield an upper limit of P_m < 7.03 × 10⁻¹¹ on the primordial power spectrum amplitude.
• The bounce scale is constrained to k_B < 2.44 × 10⁻⁴ at 2σ confidence level.
• The bounce duration parameter T is constrained to 2.63 × 10² < T < 7.98 × 10⁵ at 2σ confidence level.
• The bounce inflation model yields a Δχ² = -1.4 lower than the ΛCDM model, indicating a slightly better fit to the data.
• The model predicts a larger red tilt (n_s < 1) and enhanced primordial power compared to ΛCDM due to the bounce-induced amplitude jump.
• Contour plots show that the best-fit point for H and Δt_B is non-vanishing, suggesting a fast bounce at a very high energy scale.