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Dark Energy: Hopes and Expectations. Mario Livio Space Telescope Science Institute. What Causes Cosmic Acceleration?. Dark Energy? Standard General Relativity? Alternative Theories of Gravity?. Standard GR?. Premise: Universe not homogeneous today (fractal bubble model).

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Dark Energy: Hopes and Expectations

  • Mario Livio

  • Space Telescope Science Institute

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What Causes Cosmic Acceleration?

  • Dark Energy?

  • Standard General Relativity?

  • Alternative Theories of Gravity?

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Standard GR?

Premise: Universe nothomogeneous today (fractal bubble model).

Result: Non-linear gravitational effects, averages, local time => distance-redshift relation as observed.

Strengths: 1. No need for unseen stuff.

2. No need to change GR.

3. Could perhaps be resolved soon.

Problems: 1. Anti-Copernican (Milky Way in special place)? (Not necessarily, but different angular scales in CMB.)

2. Not clear if solution can match all observations (e.g. H0, peaks in CMB).

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Dark Energy vs. Alternative Gravity Theory

Dark Energy

  • Vacuum energy (cosmological constant), w = const. = -1

  • Scalar field,w can vary from w < -1 to w = 1

Alternative Gravity

  • Modification of Friedmann equation (5D gravity).Analogous to: w = -½ in distant past,evolving to w = -1 in distant future.

  • Purely phenomenological modifications to the GR Lagrangian.

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Alternative Gravity

Strengths: 1. Motivated by ideas from string theory.2. Testable in principle.

Weaknesses: 1. All but ruled out by lab and lunar ranging experiments

Inverse square law holds down to d = 56 m!

Measurements of lunar perihelion precession with an accuracy of δΦ = 1.4x10-12

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Alternative Gravity cont’d

2. Not clear if self-consistent model exists.

Yellow region excluded at 95% confidence level.

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Vacuum Energy

Strengths: 1. Clearly exists!2. If dark energy behaves like an ideal fluid:

Casimir Effect

This is unstable for any negative value of w, except w = -1, vacuum energy!

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Vacuum Energy (cont’d)

Problems: 1. Why so small and positive?

(But SUSY testable by LHC)

2. Why now?

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Scalar Field


  • Motivated by inflation.

  • The evolution of the fieldproduces different w(z) behavior for “freezing” or “thawing”Observations can distinguish.

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Scalar Field cont’d


  • No convincing connections to inflation.

  • Does not really explain why small and why now.

  • Choice of potential, modifications to kinetic term, rather arbitrary. In thawing models M ~ V just reflects mass of scalar field.

  • To produce acceleration, interaction of field with matter and with itself has to be extremely weak.

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Cyclic Model with Dynamical Relaxation

Cosmological constant (t) very slowly varying function, most time spent at small and positive value.

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Possibility of Multiverse?



String theory suggests that ~101000 vacua may exist.

Inflation may produce an ensemble of pocket universes.

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Possibility of Multiverse?

Fundamental Theory

  • All constants determined uniquely.

  • Examples of past successes:

    • Particle masses in QCD

    • Electroweak theory

  • Allows universes with an ensemble of values of at least some non-fundamental parameters.

  • Examples of past non-fundamental quantities:

    • Number of planets in the Solar System

    • Shapes of snowflakes

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Can A Multiverse Explain the Value of V?

If V can take a broad range of values in the multiverse, then complexity can arise only in some subuniverse. In generalV/3 is constrained.

For a flat probability distribution:

Principle of mediocrity: Is our universe typical?

By contrast, in cyclic model complexity can arise in almost every patch of space.

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Typical Objections

  • Against the scientific method?Not everything should be observable or falsifiable.Rather, if the theory is testable in the observable universe, we should be prepared to accept its predictions in the unobservable parts.

  • No predictions? Not exactly true, statistical predictions.

  • End of physics? No. Rather, modification of expectations.E.g. in mathematics: Gödel’s theorem, computational complexity.

  • Supports religion-like arguments? Absolutely not!

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Dynamical and anthropic reasoning are not mutually exclusive!

What should we do if multiverse is predicted?