[Paper Review] Triple Unification of Inflation, Dark matter and Dark energy in Chaotic Braneworld Inflation

Chia-Min Lin|ArXiv.org|Jun 26, 2009

Cosmology and Gravitation Theories4 references3 citations

TL;DR

This paper proposes a minimal model of triple unification—unifying inflation, dark matter, and dark energy—using a single scalar field in chaotic braneworld inflation. By leveraging modified Friedmann dynamics on the brane, the inflaton mass is suppressed, allowing preheating to naturally yield a field value consistent with observed dark matter density without additional mechanisms, with a viable coupling range $ g \sim 10^{-5} \text{ to } 1 $ for $ M_5/M_P \sim 10^{-11} \text{ to } 10^{-7} $.

ABSTRACT

In this paper, we show that in the framework of chaotic braneworld inflation, after preheating, the remaining oscillating inflaton field can play the role of dark matter with the observed level. Augmented by a non-zero effective cosmological constant $Λ_4$ on the brane, triple unification of inflation, dark matter and dark energy by a single field is realized. Our model perhaps is the simplest one in the market of theories to achieve triple unification.

Motivation & Objective

• To achieve a unified description of inflation, dark matter, and dark energy using a single scalar field.
• To overcome the failure of conventional chaotic inflation with preheating, where the inflaton field value after preheating is too large to match dark matter observations.
• To show that braneworld cosmology, via modified Friedmann dynamics, suppresses the inflaton mass sufficiently to allow natural dark matter relic abundance.
• To eliminate the need for additional mechanisms like thermal inflation or plasma mass effects to reduce the inflaton field value post-preheating.
• To present a minimal, self-consistent model where all three cosmic components arise from one field and one potential.

Proposed method

• Adopt the potential $ V = V_0 + \frac{1}{2}m^2\phi^2 $, where $ V_0 $ corresponds to the effective 4D cosmological constant $ \Lambda_4 $, and $ \phi $ acts as the inflaton.
• Use the modified Friedmann equation in braneworld cosmology: $ H^2 = \frac{8\pi}{3M_P^2}\rho\left(1 + \frac{\rho}{2\lambda}\right) $, which suppresses the effective inflaton mass $ m \sim 4.5 \times 10^{-5} M_5 $.
• Apply slow-roll inflation conditions and CMB normalization $ A_s \approx 2 \times 10^{-5} $ to constrain $ m $ in terms of $ M_5 $.
• Model preheating via coupling $ \frac{1}{2}g^2\phi^2\chi^2 $, reducing the inflaton field amplitude to $ \phi = m/g $ after decay.
• Use energy density and entropy conservation to derive the current dark matter-to-photon ratio $ \xi_{dm,0} \simeq 2.2 \times 10^{-28} M_P $, and match it to the post-preheating field value.
• Solve for the coupling $ g $ as a function of $ M_5/M_P $, showing $ g \sim 10^{-5} \text{ to } 1 $ for $ M_5/M_P \sim 10^{-11} \text{ to } 10^{-7} $, within viable physical ranges.

Experimental results

Research questions

• RQ1 Can a single scalar field unify inflation, dark matter, and dark energy in a minimal framework?
• RQ2 Why does conventional chaotic inflation with preheating fail to produce the correct dark matter relic abundance?
• RQ3 Can braneworld cosmology suppress the inflaton mass sufficiently to allow natural dark matter production via preheating?
• RQ4 What range of 5D Planck mass $ M_5 $ and preheating coupling $ g $ yields a consistent dark matter relic density?
• RQ5 Is an additional field reduction mechanism (e.g., thermal inflation) necessary in this unification scenario?

Key findings

• The inflaton mass is suppressed to $ m \approx 4.5 \times 10^{-5} M_5 $ due to braneworld corrections, enabling a viable dark matter relic density.
• The required preheating coupling is $ g = 5.83 \times 10^8 (M_5/M_P)^{5/4} $, which lies in the physically reasonable range $ 10^{-5} \text{ to } 1 $ for $ M_5/M_P \sim 10^{-11} \text{ to } 10^{-7} $.
• No additional field reduction mechanism (e.g., thermal inflation) is needed after preheating, as the post-preheating field value naturally matches the observed dark matter density.
• The model achieves triple unification with a single scalar field and a single potential, making it the simplest known realization of this idea.
• The effective 4D cosmological constant $ \Lambda_4 $, arising from brane tension and bulk cosmological constant, accounts for dark energy.
• The model is consistent with CMB normalization and entropy conservation, with $ \xi_{dm,0} \simeq 2.2 \times 10^{-28} M_P $, matching observational constraints.