[Paper Review] Generalized early dark energy and its cosmological consequences

Tatsuki Kodama, Takumi Shinohara+1 more|arXiv (Cornell University)|Sep 20, 2023

Cosmology and Gravitation TheoriesPhysics and Astronomy3 citations

TL;DR

This paper introduces a generalized early dark energy (EDE) model where a scalar field with power-law or axion-type potentials can dominate the universe during various epochs, depending on initial field value and energy scale. It shows that such EDE can significantly enhance the stochastic gravitational wave background, making it detectable by LISA and DECIGO, and relaxes reheating temperature bounds needed to explain the NANOGrav 15-year signal with a blue-tilted tensor spectrum.

ABSTRACT

We investigate cosmological consequences of a generalized early dark energy (EDE) model where a scalar field behaves as dark energy at various cosmological epochs for a broad range of parameters such as the energy scale and the initial field value. We consider power-law and axion-type potentials for such an EDE field and study how it affects the cosmological evolution. We show that gravitational wave background can be significantly enhanced to be detected in future observations such as LISA and DECIGO in some parameter space. Implications of the EDE model are also discussed for a scenario where a blue-tilted inflationary tensor power spectrum can explain the recent NANOGrav 15-year signal. We argue that the bounds on the reheating temperature can be relaxed compared to the case of the standard thermal history.

Motivation & Objective

• To explore cosmological consequences of a generalized early dark energy (EDE) model with broad parameter ranges for scalar field potential and initial conditions.
• To investigate how non-quadratic potentials (power-law and axion-type) affect EDE dynamics and energy density evolution.
• To assess the detectability of gravitational wave backgrounds amplified by EDE in future observatories like LISA and DECIGO.
• To examine whether EDE can alleviate the tension between the standard thermal history and the NANOGrav 15-year signal requiring a blue-tilted primordial tensor spectrum.
• To relax the stringent reheating temperature bounds required in standard models to fit the NANOGrav signal.

Proposed method

• The study employs a scalar field with power-law potential $ V(\chi) \propto \chi^p $ and axion-type potential $ V(\chi) \propto f_a^4 \left(1 - \cos(\chi/f_a)\right) $, varying the energy scale $ V_0 $, initial field value $ \chi_{\text{ini}} $, and power index $ p $.
• The cosmological evolution is simulated numerically, tracking the scalar field's energy density $ \rho_\chi \propto a^{-q} $ with $ q > 3 $, especially when $ q > 4 $, leading to rapid dilution after oscillation.
• The gravitational wave (GW) spectrum is computed using the stochastic formalism, with amplification dependent on the duration of quasi-de Sitter expansion driven by the EDE field.
• The model is constrained by requiring $ f_{\text{EDE,c}} \approx 0.01 $ and $ a_c \approx 10^{-4} $ to resolve the Hubble tension.
• The NANOGrav 15-year signal is modeled assuming inflationary GWs, and the required tensor spectral index $ n_T $ and reheating temperature $ T_R $ are recalculated with and without EDE to assess relaxation of bounds.

Experimental results

Research questions

• RQ1 How does a generalized EDE model with broad parameter ranges for initial field value and potential energy scale affect cosmological evolution and energy density dominance?
• RQ2 In what parameter space is the gravitational wave background significantly enhanced, and can it be detected by LISA and DECIGO?
• RQ3 Can the generalized EDE model reduce the required tensor spectral index $ n_T $ to fit the NANOGrav 15-year signal without violating BBN constraints?
• RQ4 How does the presence of EDE relax the reheating temperature bound required to explain the NANOGrav signal?
• RQ5 What are the implications of non-quadratic potentials (e.g., power-law, axion-type) on the dynamics and cosmological impact of early dark energy?

Key findings

• For power-law potentials, EDE with $ \chi_{\text{ini}} \approx 0.1\,M_{\text{pl}} $ and $ V_0^{1/4} \sim 10^{-9}\,\text{GeV} $ can achieve $ f_{\text{EDE,c}} \approx 0.01 $ and $ a_c \approx 10^{-4} $, satisfying Hubble tension conditions.
• For axion-type potentials, $ \chi_{\text{ini}}/f_a \approx 0.9\pi $ and $ V_0^{1/4} \sim 10^{-8}\,\text{GeV} $ yield similar EDE dominance and Hubble tension resolution.
• The gravitational wave spectrum is enhanced when EDE dominates ($ f_{\text{EDE}} > 0.5 $), with amplification primarily controlled by $ \chi_{\text{ini}} $, which determines the duration of the quasi-de Sitter phase.
• Parameter regions exist where the GW background is detectable by LISA and DECIGO, particularly for $ \chi_{\text{ini}} \gtrsim 0.1\,M_{\text{pl}} $ and low $ V_0 $, as shown in Figure 7.
• With EDE, the required tensor spectral index $ n_T $ for fitting the NANOGrav 15-year signal is reduced to $ n_T = 1.69 $ for $ p = 6 $, $ n_T = 1.62 $ for $ p = 8 $, and $ n_T = 1.59 $ for $ p = \infty $, compared to $ n_T \approx 1.8 $ in the standard model.
• The reheating temperature bound is relaxed from $ T_R < 10\,\text{GeV} $ in the standard case to $ T_R = 150\,\text{GeV} $ for $ p = 6 $, $ 400\,\text{GeV} $ for $ p = 8 $, and $ 1.59\,\text{GeV} $ for $ p = \infty $, making the model more viable.