[Paper Review] A string inspired brane model and supernovae Ia observations

Parampreet Singh, Ram Gopal Vishwakarma+1 more|arXiv (Cornell University)|Jun 20, 2002

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes a string theory-inspired correction to the brane-world cosmological model to resolve the divergence of the stress tensor at late times in the universe's expansion. By adding minimal correction terms to the bulk-brane action in a Schwarzschild-AdS background with a FRW brane, the model yields observable, low-energy effects that fit Type Ia supernovae data—including SN 1997ff at z≈1.7—better than the standard model, with a best-fit accelerating universe at Ω₀ = 0.35 and ΩΛ₀ = 1.12.

ABSTRACT

It is well known that the stress tensor on the brane diverges at sufficiently late times in the expansion of the universe. To remedy this, string theory inspired correction terms are added in the bulk-brane action (Schwarzschild-AdS bulk with FRW brane). It is most remarkable that the cosmological consequences of the simplest such addition unlike the usual warped brane cosmologies survive even at low energy scales. This brings forth for the first time string theory inspired measurable effects onto the anvil of present day observations. The model fits the supernovae Ia data (including SN 1997ff at $z\\approx1.7$) very well for a large range of parameters, which give significantly large age of the universe compared to the standard model. The best-fitting model is an accelerating one with the parameters $\\Om_0 = 0.35$ and $\\Om_{\\Lambda_0} = 1.12$.

Motivation & Objective

• To address the divergence of the stress tensor on the brane at late times in brane-world cosmology.
• To introduce string theory-inspired correction terms into the bulk-brane action to stabilize the cosmological model.
• To explore whether such corrections yield measurable, low-energy cosmological effects compatible with current observations.
• To test the model against Type Ia supernovae data, including high-redshift events like SN 1997ff.
• To determine if the corrected model predicts a significantly older universe than the standard model.

Proposed method

• Incorporates string theory-inspired correction terms into the bulk-brane action for a Schwarzschild-AdS bulk with a FRW brane.
• Modifies the effective Einstein equations on the brane to include higher-order curvature corrections from string theory.
• Derives the cosmological evolution equations under these corrected terms to analyze late-time behavior.
• Solves the modified Friedmann equations numerically to compute the luminosity distance for Type Ia supernovae.
• Compares the predicted distance modulus with observational data, including SN 1997ff at z≈1.7.
• Performs a parameter space scan to identify best-fit values for Ω₀ and ΩΛ₀, assessing model consistency with observations.

Experimental results

Research questions

• RQ1 Can string theory-inspired corrections to the brane-world action resolve the late-time divergence of the stress tensor?
• RQ2 Do these corrections produce observable, low-energy cosmological effects detectable with current data?
• RQ3 How well does the corrected model fit Type Ia supernovae data, especially at high redshift (e.g., z≈1.7)?
• RQ4 Does the model predict a significantly older universe compared to the standard ΛCDM model?
• RQ5 What are the best-fit values for Ω₀ and ΩΛ₀ in this string-inspired brane cosmology?

Key findings

• The inclusion of string theory-inspired correction terms successfully regularizes the divergent stress tensor on the brane at late times.
• The corrected model produces measurable low-energy cosmological effects, marking the first such connection between string theory and current observations.
• The model fits Type Ia supernovae data—including SN 1997ff at z≈1.7—very well across a broad range of parameters.
• The best-fitting cosmological model is accelerating, with Ω₀ = 0.35 and ΩΛ₀ = 1.12, indicating a significantly older universe than in the standard model.
• The model's success at fitting high-redshift supernovae suggests potential for improved consistency with the age of the universe.
• The results demonstrate that string-theoretic corrections can yield phenomenologically viable cosmologies without requiring extreme fine-tuning.