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Exploring Weakening Gravity: Novel Inflationary Solutions Beyond Traditional Paradigms

This paper investigates the implications of gravity weakening at short distances and its potential to support inflation in the universe. Currently, modifications of gravity tend to strengthen gravitational forces; however, we explore scenarios where gravity shuts off, seeking alternatives to the inflationary paradigm. By utilizing techniques from string theory and examining non-perturbative effects, we propose novel solutions for inflation without relying on scalar fields. The findings suggest a different relation between density perturbations and gravitational waves, which may redefine our understanding of cosmological inflation.

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Exploring Weakening Gravity: Novel Inflationary Solutions Beyond Traditional Paradigms

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  1. Fading Gravity and Self-Inflation • Justin Khoury • (Perimeter Institute) • hep-th/0610???

  2. Motivation: Widely studied modifications of gravity, e.g. large extra dimensions, typically lead to stronger gravity at short distances. 2 ways to see this: • 1. Deviation from inverse-square law: • 2. Modified Friedmann eqn in brane-world models: • Need faster expansion at fixed density in order for universe to expand forever (since k=0).

  3. BUT: What if gravity gets weaker (and shuts off) at short distances? • Can you still have inflation? • Do you need inflation? • Does it offer alternatives to the inflationary paradigm?

  4. Our idea: Shut off the graviton propagator at large momentum Non-perturbative effects in string theory (Tseytlin ‘95) Tachyon action in open string field theory p-adic string theory (Brekke, Freund, Olson, Witten ‘88) Fat Graviton scenario (Sundrum ‘97) • where • Form factor must be analytic, so no new degrees of freedom • e.g., • Find novel inflationary solutions without scalar field or other stress energy • Not equivalent to a scalar-tensor theory • Genuinely different than scalar-driven inflation

  5. Modified (horrific) Einstein’s equations: necessary to maintain Bianchi identity Effective Newton’s constant 2 key observations: 1. Pure de Sitter doesn’t care • (since ) • Thus pure dS is oblivious to form factor

  6. 2. But small deviations from dS care a lot: of order dH/dt for HL > 1 • Modified cosmological eqn roughly of the form: i.e., • Inflating solution if HL > 1

  7. More explicit sketch: • Relativistic and covariant action is: Note: as F1 theory reduces to GR • Quick check: in weak-field limit, have etc. which is action for massless spin-2 with modified propagator

  8. A fun weekend in Waterloo…. • where • with

  9. Another fun weekend in Waterloo… • Substitute FRW ansatz keeping terms at most of order dH/dt (i.e. ignoring d2H/dt2, (dH/dt)2, …). • Equations simplify tremendously and find:

  10. Exiting self-inflating phase: • Since dH/dt < 0, eventually reach F1 and inflation ends. • Moreover, recall that as F1 theory reduces to GR • Meanwhile, when dH/dt ~ H2 particle production is efficient. This is the dominant reheating mechanism here. Ford (‘87) Grishchuk & Sidorov (‘90) Spokoiny (‘93) Conjecture: graceful exit into normal radiation-dominated phase at T~L-1

  11. Perturbations: Can study evolution of fluctuations about self-inflating solution. • Density (scalar) perturbations are nearly scale-inv, with amplitude where and spectral tilt • BUT tensor spectrum is very blue Amplitude of gravity waves too small to be observed, like ekpyrotic.

  12. Robustness of effective action • Slow-evolution approximation gets better as HL • Generic corrections to effective action are less and less relevant as HL e.g. negligible compared to from form factor e.g. Effectively “renormalizes” form factor

  13. Summary and future avenues • Presented a theory where gravity shuts off at short distances • To my knowledge, theory can’t be rewritten as some scalar-tensor theory • Find novel inflationary solutions to the vacuum eqns. • Density perturbations basically degenerate with scalar-driven inf. • BUT gravity waves have blue tilt distinguishing feature from scalar infn.

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