Effects of quantum fluctuations of metric on the universe

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Effects of quantum fluctuations of metric on the
universe

• Rongjia Yang (???)
• Hebei University(????)
• Based on  arXiv1506.02889

2015.6.11,????????
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Outline

• Motivation
• Modified gravitational field equations
• Cosmological applications
• Conclusions

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Motivation
Quantized Gravity

• Canonical quantization LQG
• Path integral quantization
• Heisenberg's nonperturbative quantization

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Motivation

• Heisenberg's technique offers one possibility to
  solve this operator equation by average it over
  all possible products of the metric operator

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• Decompose the metric operator into a sum of an
  average metric and a fluctuating part

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Motivation

• The modified Lagrangian density can be written as

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Modified gravitational field equations

• We consider the simplest case

• Lagrangian density takes the form

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Modified gravitational field equations

• Varying Lagrangian density with respect to

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Modified gravitational field equations

• Assuming that the Lagrangian density of matter
  depends only on the metric tensor components

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Modified gravitational field equations

• Then we have

We obtain the gravitational field equations
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Modified gravitational field equations

• The divergence of the stress-energy tensor gives

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Cosmological applications
Considering a FLRW spacetime
and a perfect fluid specified by the stress
energy tensor
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Cosmological applications

• Taking the Lagrangian for matter as

We get the expression
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Cosmological applications

• The Friedmann equations are modified as

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Cosmological applications

• Here we consider a spatial flat FLRW spacetime

The conservation equation takes forms
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Cosmological applications

• The effects of the quantum fluctuation of metric
  on the very early universe

A bounce universe can be obtained, which can not
be realized in general relativity with normal
matter.
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Cosmological applications

• The effects of the quantum fluctuation of metric
  on inflation

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Cosmological applications

• The two slow-roll parameters are modified as

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Cosmological applications

• The spectral index and the spectrum of the
  primordial curvature perturbation are modified
  as, respectively

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Cosmological applications

• For a constant EoS,the conservation equation
  takes forms

which can be integrated as
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Cosmological applications

• For a radiation-dominated epoch

The expansion of the universe will be accelerated
even in a radiation-dominated period
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Cosmological applications

• For a dust-dominated epoch

The expansion of the universe will be accelerated
even in a dust-dominated period
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Cosmological applications

• For a dark energy dominated epoch, assuming a
  constant EoS, we find that for

A decelerated expansion will be obtained due to
the quantum fluctuations of metric
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Cosmological applications

• See, for example, taking

we find
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Cosmological applications

• See, for example, taking

we find
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Conclusions and discussions
A model of modified gravity is proposed
We have investigated effects of quantum
fluctuations of metric on the universe. Due to
the quantum fluctuations a bounce universe can be
obtained and a decelerated expansion can also
possibly be obtained even in a dark energy
dominated epoch
Other cases, see, for example,
are also worth discussing
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Thanks