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The cosmological constant and quantum vacuum. Alain Blanchard - - PowerPoint PPT Presentation

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Introduction Quantum Vacuum contribution A new scenario The cosmological constant and quantum vacuum. Alain Blanchard Arnaud Dupays, Brahim Lamine & A.B. A&A, 554 , A60 (2013) FFP14 Marseille, July 18th, 2014 Alain Blanchard The

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Introduction Quantum Vacuum contribution A new scenario

The cosmological constant and quantum vacuum.

Alain Blanchard Arnaud Dupays, Brahim Lamine & A.B. A&A, 554, A60 (2013) FFP14 Marseille, July 18th, 2014

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Accelerated expansion

There is no FL model that reproduces the present day observations without acceleration...

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Nobel Prize in Physics 2011

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Nobel Prize in Physics 2011 S.Perlmuter, A.Riess, B.Schmidt

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

What does it mean?

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

What does it mean?

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

What does it mean?

In GR, the source of gravity is ρ and P: ¨ R ∝ −(ρ + 3P)R

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

What does it mean?

In GR, the source of gravity is ρ and P: ¨ R ∝ −(ρ + 3P)R Observations need P ≈ −ρ

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

What does it mean?

In GR, the source of gravity is ρ and P: ¨ R ∝ −(ρ + 3P)R Observations need P ≈ −ρ So that the gravity strength is repulsive and proportional to R ...

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Historical aspects

Λ was introduced by Einstein

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Historical aspects

Λ was introduced by Einstein Lemaître (1934) made the comment that Λ is equivalent to a Lorentz invariant non-zero vacuum, i.e. P = −ρ (1)

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Historical aspects

Λ was introduced by Einstein Lemaître (1934) made the comment that Λ is equivalent to a Lorentz invariant non-zero vacuum, i.e. P = −ρ (1) Is there an experimental difference between Λ and L.I.V.?

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Historical aspects

Λ was introduced by Einstein Lemaître (1934) made the comment that Λ is equivalent to a Lorentz invariant non-zero vacuum, i.e. P = −ρ (1) Is there an experimental difference between Λ and L.I.V.? Nerst (1916) and Pauli discussed the possible contribution of zero-point energy to the density of the Universe (→ Kragh arXiv:1111.4623)

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Historical aspects

Λ was introduced by Einstein Lemaître (1934) made the comment that Λ is equivalent to a Lorentz invariant non-zero vacuum, i.e. P = −ρ (1) Is there an experimental difference between Λ and L.I.V.? Nerst (1916) and Pauli discussed the possible contribution of zero-point energy to the density of the Universe (→ Kragh arXiv:1111.4623)

So is this the origin of the acceleration ?

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Historical aspects

No!

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Historical aspects

No!

The Vacuum catastroph (Weinberg, 1989): ρv = 0|T 00|0 = 1 (2π)3 +∞ 1 2ω d3k with ω2 = k2 + m2

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Historical aspects

No!

The Vacuum catastroph (Weinberg, 1989): ρv = 0|T 00|0 = 1 (2π)3 kc 1 2ω d3k with ω2 = k2 + m2 highly divergent: ρv(kc) ∝ k4

c

16π2 (for kc ≫ m).

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Equation of state

The pressure (massless field): Pv = (1/3)

  • i

0|T ii|0 = 1 3 1 2(2π)3 +∞ k d3k

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Equation of state

The pressure (massless field): Pv = (1/3)

  • i

0|T ii|0 = 1 3 1 2(2π)3 +∞ k d3k So that any regularization that is applied to both quantities leads to the e.o.s.:

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Equation of state

The pressure (massless field): Pv = (1/3)

  • i

0|T ii|0 = 1 3 1 2(2π)3 +∞ k d3k So that any regularization that is applied to both quantities leads to the e.o.s.: P = 1 3ρ (2)

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Equation of state

The pressure (massless field): Pv = (1/3)

  • i

0|T ii|0 = 1 3 1 2(2π)3 +∞ k d3k So that any regularization that is applied to both quantities leads to the e.o.s.: P = 1 3ρ (2) i.e. eq. (1) + eq. (2) leads to : Pv = ρv = 0

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Equation of state

The pressure (massless field): Pv = (1/3)

  • i

0|T ii|0 = 1 3 1 2(2π)3 +∞ k d3k So that any regularization that is applied to both quantities leads to the e.o.s.: P = 1 3ρ (2) i.e. eq. (1) + eq. (2) leads to : Pv = ρv = 0 → usual conclusion on zero-point energy contribution (for instance by dimensional regularization).

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Equation of state

Does not hold for a massive field (Zeldovich 1968, ...): Pv = −ρv

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Equation of state

Does not hold for a massive field (Zeldovich 1968, ...): Pv = −ρv But ρv = m4(...)

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Equation of state

Does not hold for a massive field (Zeldovich 1968, ...): Pv = −ρv But ρv = m4(...) cf Review by J.Martin 2012 (astro-ph/1205.3365).

Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect

Where is there vacuum contribution in laboratory physics?

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect

Where is there vacuum contribution in laboratory physics? Casimir effect

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect

Where is there vacuum contribution in laboratory physics? Casimir effect with (assuming ρext = 0): Px = 3ρ

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect

Where is there vacuum contribution in laboratory physics? Casimir effect with (assuming ρext = 0): Px = 3ρ < 0

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect

Where is there vacuum contribution in laboratory physics? Casimir effect with (assuming ρext = 0): Px = 3ρ < 0 and ...

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect

Where is there vacuum contribution in laboratory physics? Casimir effect with (assuming ρext = 0): Px = 3ρ < 0 and ... P// = −ρ Brown & Maclay (1968)

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect from higher dimension

Assume there is an additional compact dimension.

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect from higher dimension

Assume there is an additional compact dimension. Standard physics in 3+1 D (brane), gravity in 3+1+1D (Bulk).

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect from higher dimension

Assume there is an additional compact dimension. Standard physics in 3+1 D (brane), gravity in 3+1+1D (Bulk). The quantification of gravitational field modes in the bulk leads to a Casimir energy (Appelquist & Chodos, 1983).

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect from higher dimension

Assume there is an additional compact dimension. Standard physics in 3+1 D (brane), gravity in 3+1+1D (Bulk). The quantification of gravitational field modes in the bulk leads to a Casimir energy (Appelquist & Chodos, 1983). This result can be established by evaluating zero mode contributions (Rohrlich 1984). Dispersion relation: ω2 = k2 + n2 R2

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect from higher dimension

Assume there is an additional compact dimension. Standard physics in 3+1 D (brane), gravity in 3+1+1D (Bulk). The quantification of gravitational field modes in the bulk leads to a Casimir energy (Appelquist & Chodos, 1983). This result can be established by evaluating zero mode contributions (Rohrlich 1984). Dispersion relation: ω2 = k2 + n2 R2 This (permanent) contribution can be evaluated by mean of dimensional regularization. But : ρ < 0

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect: the Hubble radius

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect: the Hubble radius

Assumption 1: At high energy, only modes with λ smaller than ct have to be taken into account i.e.: ρv = 5c 8π3R ∞

ω>ωH

k2dk

  • ∞
  • n=−∞
  • k2 + n2

R2 1/2

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Casimir effect: the Hubble radius

Assumption 1: At high energy, only modes with λ smaller than ct have to be taken into account i.e.: ρv = 5c 8π3R ∞

ω>ωH

k2dk

  • ∞
  • n=−∞
  • k2 + n2

R2 1/2 Assumption 2: as long as ct ≪ πR gravitational vacuum should be that of a massless field in a 4+1D space time i.e.: ρv = 0

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Space Isotropy ends...

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Space Isotropy ends...

when ct ∼ πR ωH ∼ 1

R , this is the last time at which

symetries ensure ρv = 0. Then ρv = 5c 8π3R ∞

1/R

k2dk [...] = 0

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Space Isotropy ends...

when ct ∼ πR ωH ∼ 1

R , this is the last time at which

symetries ensure ρv = 0. Then ρv = 5c 8π3R ∞

1/R

k2dk [...] = 0 Later, when ct ≫ πR i.e. ωH ∼ 0 ρv = 5c 8π3R ∞ k2dk [...] = 5c 8π3R 1/R k2dk [...] with : [...] =

  • ∞
  • n=−∞
  • k2 + n2

R2 1/2

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Isotropy ends...

The condition : ω =

  • k2 + n2

R2 < 1 R ensured only if n = 0, so: ρv = 5c 8π3R 1/R k3dk = 5c 32π3R5

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Isotropy ends...

The condition : ω =

  • k2 + n2

R2 < 1 R ensured only if n = 0, so: ρv = 5c 8π3R 1/R k3dk = 5c 32π3R5 In the brane: ρv = 5c 16π2R4

Alain Blanchard The cosmological constant and quantum vacuum.

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Dark energy emerges...

Pressure: P⊥

v = 4ρ0 =

20c 32π3R5 Along the brane, using the fact that the T µν is traceless and integrating along the 4th spatial dimension: P

v = −

5c 16π2R4 = −ρv

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Dark energy emerges...

Pressure: P⊥

v = 4ρ0 =

20c 32π3R5 Along the brane, using the fact that the T µν is traceless and integrating along the 4th spatial dimension: P

v = −

5c 16π2R4 = −ρv so: R = 5G 2πcΛ 1

4 Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Dark energy emerges...

Pressure: P⊥

v = 4ρ0 =

20c 32π3R5 Along the brane, using the fact that the T µν is traceless and integrating along the 4th spatial dimension: P

v = −

5c 16π2R4 = −ρv so: R = 5G 2πcΛ 1

4

Ωv ∼ 0.7 ⇒ R ∼ 35µm fits data. Corresponding to E ∼ 1TeV

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Consequences

Acceleration is due to vacuum: GR + w = −1

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Consequences

The presence of additional compact “large” dimension (∼ 35µm) can be tested by experiment on gravitational inverse square law on short scale. Additional term:

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Consequences

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Consequences

Present day limit (Kapner et al. 2007; Adelberger et al. 2009) :

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Testing the idea

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Testing the idea

R < 46µm

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Conclusion

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Conclusion

◮ Casimir effect from quantized scalar field in additional

compact dimension can produce a non-zero vacuum contribution to the density of the universe with the correct equation of state for a cosmological constant. i.e. “usual” physics for DE.

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Conclusion

◮ Casimir effect from quantized scalar field in additional

compact dimension can produce a non-zero vacuum contribution to the density of the universe with the correct equation of state for a cosmological constant. i.e. “usual” physics for DE.

◮ Acceleration could be the direct manifestation of the

quantum gravitational vacuum.

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Conclusion

◮ Casimir effect from quantized scalar field in additional

compact dimension can produce a non-zero vacuum contribution to the density of the universe with the correct equation of state for a cosmological constant. i.e. “usual” physics for DE.

◮ Acceleration could be the direct manifestation of the

quantum gravitational vacuum.

◮ With R ∼ 35µm it produces a cosmological constant as

  • bserved.

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Conclusion

◮ Casimir effect from quantized scalar field in additional

compact dimension can produce a non-zero vacuum contribution to the density of the universe with the correct equation of state for a cosmological constant. i.e. “usual” physics for DE.

◮ Acceleration could be the direct manifestation of the

quantum gravitational vacuum.

◮ With R ∼ 35µm it produces a cosmological constant as

  • bserved. → gravitation is modified on scales ≤ 45µm

Alain Blanchard The cosmological constant and quantum vacuum.

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Introduction Quantum Vacuum contribution A new scenario

Conclusion

◮ Casimir effect from quantized scalar field in additional

compact dimension can produce a non-zero vacuum contribution to the density of the universe with the correct equation of state for a cosmological constant. i.e. “usual” physics for DE.

◮ Acceleration could be the direct manifestation of the

quantum gravitational vacuum.

◮ With R ∼ 35µm it produces a cosmological constant as

  • bserved. → gravitation is modified on scales ≤ 45µm

◮ → Testable!

Alain Blanchard The cosmological constant and quantum vacuum.