Dynamical cosmic vacuum in the Universe Adrià Gómez-Valent PhD student under the supervision of
Prof. Joan Solà
ISSP
Erice, Italy, 17th June 2016
The accelerating universe • 1998: Accurate measurement of the luminosity distance-redshift curve of distant SnIa carried out by the Supernova Cosmology Project and the High-z Supernova Search Team.
Our Universe is speeding up! The so-called concordance ΛCDM model fits well the data. A positive rigid Λ could explain the 70% of the energy content of the universe.
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Some details on the cosmological costant (CC) The CC behaves like vacuum
Easy interpretation from the thermodynamical point of view.
Universe box expanding adiabatically
Due to its negative pressure, the CC has repulsive gravitational power!
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Existing problems
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Existing problems • How can theory explain the observed tiny value of the CC?
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Existing problems • How can theory explain the observed tiny value of the CC?
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
4
Existing problems • How can theory explain the observed tiny value of the CC?
Several contributions to the this energy density:
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Existing problems • How can theory explain the observed tiny value of the CC?
Several contributions to the this energy density:
I.
Zero-point energy
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
4
Existing problems • How can theory explain the observed tiny value of the CC?
Several contributions to the this energy density:
I.
Zero-point energy
II.
Electroweak vacuum
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
4
Existing problems • How can theory explain the observed tiny value of the CC?
Several contributions to the this energy density:
I.
Zero-point energy QFT contributions
II.
Electroweak vacuum
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
4
Existing problems • How can theory explain the observed tiny value of the CC?
Several contributions to the this energy density:
I.
Zero-point energy QFT contributions
II.
Electroweak vacuum
III. Pure geometrical term in the lhs of Einstein’s equations Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
4
Existing problems • How can theory explain the observed tiny value of the CC?
Several contributions to the this energy density:
I.
Zero-point energy
II.
Electroweak vacuum
Fine tuning is needed! Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
4
Existing problems • How can theory explain the observed tiny value of the CC?
Several contributions to the this energy density:
I.
Zero-point energy
II.
Electroweak vacuum
Fine tuning is needed! Adrià Gómez-Valent
OLD COSMOLOGICAL CONSTANT PROBLEM
Dynamical cosmic vacuum in the Universe
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Existing problems • Why is the current value of the matter energy density of the same order of the vacuum energy density?
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Existing problems • Why is the current value of the matter energy density of the same order of the vacuum energy density?
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Existing problems • Why is the current value of the matter energy density of the same order of the vacuum energy density?
Density equality at z≈0.33, when the Universe was ≈10 Gyrs old, almost 4 Gyrs ago.
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Different approaches to alleviate the existing problems • Scalar field theories: k-essence (quintessence, phantom field, etc.)
• Scalar-tensor gravity, i.e. Brans-Dicke theory.
• Chaplygin gas
• Modified gravity theories, i.e. f(R) gravity. • ΛXCDM cosmon models. • Dynamical vacuum in QFT in curved space-time. 6
Different approaches to alleviate the existing problems • Scalar field theories: k-essence (quintessence, phantom field, etc.)
• Scalar-tensor gravity, i.e. Brans-Dicke theory.
• Chaplygin gas
• Modified gravity theories, i.e. f(R) gravity. • ΛXCDM cosmon models. • Dynamical vacuum in QFT in curved space-time. 6
MODEL INDEPENDENT EVIDENCE FOR DARK ENERGY EVOLUTION • Reference: Sahni, V., Shafieloo, A., & Starobinsky, A. A., 2014, ApJL, 793 L40 (arXiv:1406.2209)
• Their Diagnostic:
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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MODEL INDEPENDENT EVIDENCE FOR DARK ENERGY EVOLUTION • Reference: Sahni, V., Shafieloo, A., & Starobinsky, A. A., 2014, ApJL, 793 L40 (arXiv:1406.2209)
• Their Diagnostic:
• In the ΛCDM:
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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MODEL INDEPENDENT EVIDENCE FOR DARK ENERGY EVOLUTION • Reference: Sahni, V., Shafieloo, A., & Starobinsky, A. A., 2014, ApJL, 793 L40 (arXiv:1406.2209)
• Their Diagnostic:
• In the ΛCDM:
Planck 2015
Adrià Gómez-Valent
Using the available Hubble function data set
Dynamical cosmic vacuum in the Universe
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MODEL INDEPENDENT EVIDENCE FOR DARK ENERGY EVOLUTION • Reference: Sahni, V., Shafieloo, A., & Starobinsky, A. A., 2014, ApJL, 793 L40 (arXiv:1406.2209)
• Their Diagnostic:
• In the ΛCDM:
Using the available Hubble function data set
Planck 2015
≠ Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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MODEL INDEPENDENT EVIDENCE FOR DARK ENERGY EVOLUTION • Reference: Sahni, V., Shafieloo, A., & Starobinsky, A. A., 2014, ApJL, 793 L40 (arXiv:1406.2209)
• Their Diagnostic:
• In the ΛCDM:
Planck 2015
Using the available Hubble function data set
≠ Probably, Λ must be dynamical Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Possible consequences of the variation of Λ Bianchi identity Einstein’s equations
Covariant conservation laws For ν=0
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Possible consequences of the variation of Λ I: G is constant and matter exchanges energy with the vacuum. • Gómez-Valent A., Solà J. & Basilakos S., 2015, J. Cosmol. Astropart. Phys. 0402, 006 ; Gómez-Valent A. & Solà J.,2015, Mont. Not. Roy. Astron. Soc. 448, 28102821. • Solà, J., Gómez-Valent A., & De Cruz Pérez, J., arXiv: 1602.02103 . • Solà, J., Gómez-Valent A., & De Cruz Pérez, J., Nunes, R.C., arXiv:1606.00450 .
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Possible consequences of the variation of Λ II: G is time-dependent and matter is covariantly conserved. • Solà, J., Gómez-Valent, A., & De Cruz Pérez, J., 2015, ApJ, 811, L14
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Possible consequences of the variation of Λ II: G is time-dependent and matter is covariantly conserved. • Solà, J., Gómez-Valent, A., & De Cruz Pérez, J., 2015, ApJ, 811, L14
• III: I+II
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Possible consequences of the variation of Λ I: G is constant and matter exchanges energy with the vacuum. • Gómez-Valent A., Solà J. & Basilakos S., 2015, J. Cosmol. Astropart. Phys. 0402, 006 ; Gómez-Valent A. & Solà J.,2015, Mont. Not. Roy. Astron. Soc. 448, 2810-2821. • Solà, J., Gómez-Valent A., & De Cruz Pérez, J., arXiv: 1602.02103 . • Solà, J., Gómez-Valent A., & De Cruz Pérez, J., Nunes, R.C., arXiv:1606.00450 .
II: G is time-dependent and matter is covariantly conserved. • Solà, J., Gómez-Valent, A., & De Cruz Pérez, J., 2015, ApJ, 811, L14 III: I+II Adrià Gómez-Valent
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β function for Λ Renormalization Group Equation:
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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β function for Λ Renormalization Group Equation:
Adrià Gómez-Valent
Some References: I.L. Shapiro & J. Solà, JHEP 0202 (2002) 006 J. Solà, J.Phys. A41 (2008) 164066 I.L. Shapiro & J. Solà, Phys.Lett. B682 (2009) 105-113 J. Solà, J.Phys.Conf.Ser. 453 (2013) 012015
Dynamical cosmic vacuum in the Universe
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β function for Λ Renormalization Group Equation:
Some References: I.L. Shapiro & J. Solà, JHEP 0202 (2002) 006 J. Solà, J.Phys. A41 (2008) 164066 I.L. Shapiro & J. Solà, Phys.Lett. B682 (2009) 105-113 J. Solà, J.Phys.Conf.Ser. 453 (2013) 012015
After identifying μ with the Hubble function and integrating we find:
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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β function for Λ Renormalization Group Equation:
Some References: I.L. Shapiro & J. Solà, JHEP 0202 (2002) 006 J. Solà, J.Phys. A41 (2008) 164066 I.L. Shapiro & J. Solà, Phys.Lett. B682 (2009) 105-113 J. Solà, J.Phys.Conf.Ser. 453 (2013) 012015
After identifying μ with the Hubble function and integrating we find:
LOW-ENERGY LIMIT
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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β function for Λ Renormalization Group Equation:
Some References: I.L. Shapiro & J. Solà, JHEP 0202 (2002) 006 J. Solà, J.Phys. A41 (2008) 164066 I.L. Shapiro & J. Solà, Phys.Lett. B682 (2009) 105-113 J. Solà, J.Phys.Conf.Ser. 453 (2013) 012015
After identifying μ with the Hubble function and integrating we find:
LOW-ENERGY LIMIT The higher derivative terms are important during inflation. See the references: J.A.S Lima, S. Basilakos, & J. Solà, MNRAs, Mon. Not. Roy. Astron. Soc 431 (2013) 923; Gen. Rel. Grav. 47 (2015) 40; Eur. Phys. J. C 76 (2016) 228. Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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RVM model. Background solutions We consider
Adrià Gómez-Valent
interacting with dark matter.
Dynamical cosmic vacuum in the Universe
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RVM model. Background solutions We consider
Adrià Gómez-Valent
interacting with dark matter.
Dynamical cosmic vacuum in the Universe
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RVM model. Background solutions We consider
interacting with dark matter.
with
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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RVM model. Background solutions We consider
interacting with dark matter.
with
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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RVM model. Background solutions Energy densities Radiation
Baryons
Dark matter Vacuum
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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RVM model. Background solutions Energy densities Radiation
Baryons
Dark matter Vacuum Of course, all the background functions reduce to the ΛCDM ones in the limit ν=0 . Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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RVM model. Linear structure formation The differential equation that governs the behavior of the matter perturbations at the linear level is:
with
Initial conditions (z≈100):
Adrià Gómez-Valent
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Fitting analysis Cosmological observables used in the fitting analysis: 1. JLA set of Ia supernovae of Betoule et al. (2014).
2. BAO data 3. CMB R shift parameter and acoustic length with the covariance matrix of the compressed likelihood analysis for Planck 2015 TT+TE+E+lowP data.
Adrià Gómez-Valent
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Fitting analysis 4. 30 Hubble points obtained with the differential age method. 5. LSS formation data
Adrià Gómez-Valent
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Main results. Best-fit values
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Main results. Best-fit values
Phenomenological models:
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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Main results. Best-fit values
Phenomenological models:
Recall that... RVM:
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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The Akaike and Bayesian information criteria • Model selection criteria • They penalize the use of extra parameters in the model • Given two competing models describing the same data, the model that does better is the one with smaller AIC and BIC values. • For 𝑁 observational points and 𝑛 fit parameters they read:
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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The Akaike and Bayesian information criteria • Model selection criteria • They penalize the use of extra parameters in the model • Given two competing models describing the same data, the model that does better is the one with smaller AIC and BIC values. • For 𝑁 observational points and 𝑛 fit parameters they read:
BIC criterion is more stringent than the AIC
Adrià Gómez-Valent
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The Akaike information criterion Rule of thumb:
• Δ𝑖𝑗 < 2 • 6 ≥ Δ𝑖𝑗 ≥ 2 • 6 ≤ Δ𝑖𝑗
Adrià Gómez-Valent
no evidence strong evidence very strong evidence
Dynamical cosmic vacuum in the Universe
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The Bayesian information criterion Rule of thumb: • Δ𝑖𝑗 < 2.5 • 5 ≥ Δ𝑖𝑗 ≥ 2.5 • 10 ≥ Δ𝑖𝑗 ≥ 5 • 10 ≤ Δ𝑖𝑗
Adrià Gómez-Valent
no evidence weak evidence strong evidence very strong evidence
Dynamical cosmic vacuum in the Universe
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Main results. Best-fit values Evidence in favour of the dynamical vacuum models!
Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
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RVM model. Linear structure formation The dynamical vacuum models are able to fit fit better the linear structure formation data.
Adrià Gómez-Valent
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Main results. Contour lines
ΛCDM is disfavored at ≈4σ c.l.
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Summary 1.
We have analyzed some dynamical vacuum models. We have focused our attention on the RVM, in which the vacuum energy density depends functionally on the Hubble rate. It is motivated from RG arguments in QFT in curved space-time.
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These kind of models are able to fit considerably better the current observational data than the concordance ΛCDM one at a confidence level of 4σ.
3.
If dark energy is vacuum-like, then the data strongly prefer a mildly evolving Λ.
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Thank you very much for your attention
[email protected] Adrià Gómez-Valent
Dynamical cosmic vacuum in the Universe
