Fading Gravity and Self-Inflation

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.