[Paper Review] Large tensor-to-scalar ratio and low scale inflation

Rouzbeh Allahverdi, Anupam Mazumdar+1 more|ArXiv.org|Dec 12, 2007

Cosmology and Gravitation Theories2 references4 citations

TL;DR

This paper proposes a two-phase inflation model where high-scale assisted inflation at ~10¹³ GeV generates large tensor-to-scalar ratio gravity waves, while low-scale MSSM inflation at ~1 GeV produces scalar perturbations and reheats the universe into SM baryons and dark matter. The tensor modes from the first phase 'trickle through' the horizon of the second phase, resulting in a strongly red-tilted tensor spectrum with r_observed ≤ 0.8, observable only at the largest angular scales (l ≈ 2).

ABSTRACT

It is plausible that the scalar density perturbations are created by a relatively low scale model of inflation which predicts the CMB anisotropy and excites Standard Model baryon and cold dark matter, but negligible gravity waves. Nevertheless a significantly large tensor perturbations can be observed if there exists a prior phase of high scale inflation separated by a matter or radiation dominated epoch. In this paper we provide a simple example when the gravity waves generated at high scales trickle through the horizon of the second phase of inflation and leave a distinct imprint in the spectrum of the tensor modes. For a high scale inflation occurring at $H\sim 10^{13}$ GeV while the second phase of inflation happening at $H\sim 1$ GeV, the largest tensor to scalar ratio is bounded by $r_{ m observed}\leq0.8$.

Motivation & Objective

• To generate a large tensor-to-scalar ratio (r) in a realistic particle physics context without requiring super-Planckian inflaton VEVs.
• To ensure scalar density perturbations originate solely from a low-scale inflation phase (H ~ 1 GeV) to avoid breaks in the CMB power spectrum.
• To achieve automatic reheating into SM baryons and cold dark matter via MSSM inflation, avoiding ad hoc couplings.
• To enable observable gravity waves from a high-scale phase to imprint distinct features on the largest angular scales.

Proposed method

• Use a two-phase inflation scenario: first phase driven by n scalar fields with V = ∑m²χᵢ² (assisted inflation at H ~ 10¹³ GeV), followed by a matter-dominated epoch.
• Introduce a second phase of MSSM inflation at H ~ 1 GeV, which generates all scalar perturbations and reheats the universe into SM and dark matter.
• Model the evolution of tensor and scalar modes across the transition, accounting for horizon reprocessing and phase differences due to changing equation of state.
• Apply the Mukhanov-Sasaki formalism to compute power spectra, with tensor modes from the first phase reprocessed during the second phase.
• Use the critical mode k_c (corresponding to the current horizon) to determine the observed tensor-to-scalar ratio, with r_observed ≤ 0.8 for H_assist ~ 10¹³ GeV.
• Analyze the correlation structure: tensor and scalar modes are anti-correlated on large scales due to differing oscillation onset times, leading to a ∼k⁻⁶ power spectrum for tensor modes.

Experimental results

Research questions

• RQ1 Can a large tensor-to-scalar ratio be generated in a low-scale inflation model without super-Planckian inflaton VEVs?
• RQ2 Can gravity waves from a high-scale inflation phase imprint a detectable signal on the largest angular scales after passing through a low-scale inflation phase?
• RQ3 Can scalar perturbations arise exclusively from a low-scale MSSM inflation phase, preserving a smooth CMB power spectrum without breaks?
• RQ4 How do the relative phases of tensor and scalar modes evolve across the transition from matter domination to low-scale inflation, and what observable imprints do they leave?
• RQ5 What is the maximum observable tensor-to-scalar ratio in a two-phase inflation model with high-scale assisted inflation and low-scale MSSM inflation?

Key findings

• The observed tensor-to-scalar ratio is bounded by r_observed ≤ 0.8 for H_assist ~ 10¹³ GeV and H_MSSM ~ 1 GeV, with the signal confined to the largest angular scales (l ≈ 2).
• The tensor power spectrum exhibits a strong red tilt, scaling as ∼k⁻⁶, due to reprocessing of high-scale gravity waves through the horizon of the second inflationary phase.
• Scalar and tensor modes are anti-correlated on large scales (k < k_c) due to different onset times of oscillations, leading to a distinctive imprint in the CMB correlation functions.
• For modes deeper inside the horizon (k > k_c), scalar and tensor modes become correlated, with power spectra scaling as ∼k⁻⁵, distinguishing this scenario from single-phase inflation.
• The model naturally provides initial conditions for MSSM inflation: high-scale assisted inflation pushes the MSSM flat direction to φ₀ ~ 10¹⁴ GeV within ~80 e-foldings.
• Future CMB experiments may distinguish this scenario from single-phase inflation by detecting the sharp drop in tensor correlations at small angular scales and the red-tilted spectrum.