[Paper Review] Stronger gravity in the early universe

M. Yoshimura|arXiv (Cornell University)|Apr 25, 2022

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes that conformal gravity models with an inflaton-coupled scalar field predict significantly stronger gravity in the early universe, especially in cold dark matter clumps dominated by inflaton fields. By modifying the standard model Lagrangian in the Jordan frame to preserve nucleosynthesis constraints, the work shows that gravitational strength scales as (z+1)^8 for CDM clumps, enhancing primordial gravitational wave emission and primordial black hole formation beyond general relativity predictions.

ABSTRACT

Scalar-tensor theories of gravity that embrace conformal coupling to the scalar curvature are the focal point of cosmology on discussions of inflation and late-time accelerating universe. Although there exists a stringent nucleo-synthesis constraint on conformal gravity, one can formulate how to evade this difficulty by modifying the standard particle theory action consistently with the principles of gauge invariant quantum field theory. It is shown that stronger gravity at early epochs of cosmological evolution than previously thought of is inevitable in a class of conformal gravity models. This enhances discovery potentials of primordial gravitational wave emission and primordial black hole formation. The strong gravity effect may be enormous if massive clumps are energetically dominated by cold dark matter made of inflaton field, and created black holes may become a major candidate of cold dark matter.

Motivation & Objective

• To resolve the fine-tuned cosmological constant problem within a unified scalar-tensor gravity framework that also explains inflation and late-time acceleration.
• To address the stringent nucleosynthesis constraint on proton-to-W-boson mass ratio variation, which restricts conformal gravity models.
• To formulate a consistent modification of the standard model Lagrangian in the Jordan frame that preserves gauge invariance and quantum field theory principles.
• To explore the implications of enhanced gravity in early-universe clumps, particularly those dominated by inflaton-based cold dark matter.
• To identify observable signatures—such as enhanced gravitational wave emission and primordial black hole formation—for testing strong gravity effects in the early universe.

Proposed method

• Formulates a scalar-tensor gravity model in the Jordan frame with a conformal coupling function $ F(\chi) $, where $ \chi $ is the inflaton field, and includes a positive cosmological constant $ \Lambda $.
• Applies a Weyl rescaling to transform the theory into the Einstein frame, where the Planck mass $ M_{\rm P} $ is constant, and the effective gravitational coupling becomes $ G_N \propto F^{-1}(\chi) $.
• Derives the effective potential $ V_{\rm eff}^{(E)}(\chi) $ in the Einstein frame using a variational principle under a spatially homogeneous FRW metric, incorporating non-minimal coupling effects.
• Introduces a modified standard model Lagrangian in the Jordan frame to preserve nucleosynthesis constraints, ensuring the proton-to-W-boson mass ratio remains constant during cosmic evolution.
• Analyzes the time evolution of the inflaton field $ \chi $, assuming $ \chi \propto (z+1)^{-2} $, leading to $ F(\chi) \propto \chi^{-2} \propto (z+1)^4 $, which drives strong gravity at high redshifts.
• Computes the effective gravitational strength $ G_N M^2 \propto F^{-2}(\chi) \propto (z+1)^8 $ for clumps dominated by inflaton-based cold dark matter, and $ G_N M^2 \propto F^{-4\epsilon}(\chi) \propto (z+1)^{16\epsilon} $ for baryonic clumps, depending on the coupling parameter $ \epsilon $.

Experimental results

Research questions

• RQ1 Can conformal gravity models with a dynamical inflaton field consistently evade nucleosynthesis constraints while allowing for varying gravitational strength?
• RQ2 What is the quantitative enhancement of gravitational strength in early-universe clumps dominated by inflaton-based cold dark matter compared to general relativity?
• RQ3 How does the redshift dependence of gravitational wave emission and primordial black hole formation scale in these models, particularly for CDM-dominated clumps?
• RQ4 What observational signatures—such as frequency distributions of gravitational wave events—can distinguish primordial black hole formation from astrophysical origins?
• RQ5 How does the choice of coupling parameter $ \epsilon $ affect the growth of gravitational strength in baryonic versus CDM-dominated structures?

Key findings

• The effective gravitational strength for cold dark matter clumps made of inflaton fields scales as $ G_N M^2 \propto (z+1)^8 $, leading to an enormous enhancement at high redshifts.
• For baryonic clumps, the gravitational strength grows as $ G_N M^2 \propto (z+1)^{16\epsilon} $, which becomes significant only if $ \epsilon > 0 $ and not too small.
• The model predicts much stronger primordial gravitational wave emission and copious primordial black hole formation than general relativity, especially in CDM-dominated clumps.
• Even a small Gaussian tail in the initial mass function of CDM clumps can lead to strong gravitational collapse due to the $ (z+1)^8 $ scaling of gravity.
• The total primordial black hole abundance is limited to $ O({\rm meV})^4 $, ensuring they do not overclose the universe, consistent with observational bounds.
• High-statistics observations of gravitational waves from neutron star mergers at different redshifts may provide a test of the $ \epsilon $ parameter through the redshift-dependent scaling $ G_N M_{\rm NS}^2 (z+1)^{16\epsilon} $.