1
|
- Neven Bilić
- Zavod za teorijsku fiziku
- Institut Ruđer Bošković
|
2
|
- Homogenost i izotropnost prostora
- Materija u obliku tzv. idealnog fluida
- um -četverovektor
brzine
- Tmn- tenzor energije-impulsa
|
3
|
|
4
|
|
5
|
- Kozmološka konstanta L
= gustoća
energije vakuuma
- Ubrzano širenje omogućuje negativni tlak energije vakuuma!
- Novi pojam: Tamna Energija (Dark Energy)
- kozmička supstanca
negativnog tlaka
- Ubrzano širenje i usporedba standardnog Big Bang modela s opažanjima
zahtjeva da gustoća energije vakuuma rL= 70% rcr
|
6
|
- kozmološka konstanta – gustoća energije vakuuma ne mijenja se s
vremenom
- kvintesencija - novo polje - gustoća energije mijenja se s vremenom
- kvartesencija - model ujedinjenja tamne energije i tamne materije
- Fantomska energija – negativni tlak prevazilazi gustoću energije –
Big Rip – potpuni raspad svih vezanih sustava
|
7
|
|
8
|
- Scalar field θ with selfinteraction
- Equvalent to a perfect fluid
|
9
|
- where
- A suitable choice of the kinetic term K
- and the potetial V yields a desired cosmology.
- Or vice versa: from a desired eq.
of state
- p=p(ρ) one can derive the Lagrangian
|
10
|
- An exotic fluid with an equation of state
- The first definite model for a dark matter/energy
- unification
- A. Kamenshchik, U.
Moschella, V. Pasquier, PLB 511
(2001)
- N.B., G.B. Tupper, R.D.
Viollier, PLB 535 (2002)
- J.C. Fabris, S.V.B.
Goncalves, P.E. de Souza, GRG 34 (2002)
|
11
|
- The generalized Chaplygin gas
- M.C. Bento, O. Bertolami, and A.A. Sen, PRD 66 (2002)
|
12
|
- The Chaplygin gas model is equivalent to the (scalar) Dirac-Born-Infeld
description of a D-brane
- R. Jackiw, Lectures on Fluid Mechanics (Springer, 2002)
- String theory branes possess three features that are absent in the
simple Nambu Goto p-dim membranes
- (i) support an Abelian gauge
field Aμ reflecting open strings with their ends stuck
on the brane;
- (ii) couple to the dilaton Φ
- (iii) couple to the (pull-back of)
- Kalb-Ramond field Bμν
|
13
|
- the induced metric (“pull back”
of the
- bulk metric)
|
14
|
|
15
|
- If we neglect the dilaton and the B-field, we find
- perfect fluid
|
16
|
- and hence
- In a homogeneous model the conservation equation yields the
- Chaplygin gas density as a function of the scale factor a
- where B is an integration constant.The Chaplygin gas thus interpolates
- between dust (ρ~a -3 ) at large redshifts and a
cosmological constant
- (ρ~ A˝) today and hence yields a correct homogeneous
cosmology
|
17
|
|
18
|
|
19
|
|
20
|
- The physical reason is that
although the adiabatic speed of
sound
- is small until a ~ 1, the accumulated comoving acoustic
horizon
- reaches MPc scales by redshifts
of twenty, frustrating the structure formation even into a mildly
nonlinear regime
|
21
|
- the density contrast described
by a nonlinear evolution equation either grows as dust or undergoes
damped oscillations depending on the initial conditions
|
22
|
- The root of the structure
formation problem is the last term, as may be understood if we solve the
equation at linear order
- with the solution (in k-space)
- Hence damped oscillations at
the scales below ds
|
23
|
- If there are entropy
perturbations such that the pressure perturbation δp=0 and with it the acoustic horizon ds=0,
no problem arises
- R.R.R. Reis, I. Waga,
M.O. Calvăo, and S.E. Joŕas,
PRD 68 (2003)
- The scenario with entropy
perturbations, which is difficult to justify in the simple Chaplygin gas model, may be realized
by introducing an extra degree of freedom, e.g., in terms of a
quintessence-type scalar field φ
|
24
|
- Suppose that the matter
Lagrangian depends on two degrees of freedom, e.g., a Born-Infeld scalar
field θ and one additional scalar field φ. In this case,
instead of a simple barotropic form p=p(ρ), the equation of state involves the
entropy density (entropy per particle) s and may be written in the parametric form
- p=p(θ,φ) s=s(θ,φ)
- The corresponding perturbations
|
25
|
- The speed of sound is the sum
of two nonadiabatic terms
- Thus, even for a nonzero ∂p/∂r the speed of sound may vanish if the second term on the
right-hand side cancels the first
one. This cancellation will take place if in the course of an adiabatic
expansion, the perturbation δφ grows with a in the same way as δr . In this case, it is only a
matter of adjusting the initial conditions of δφ with δr to get cs=0.
|
26
|
- The DBI theory which we started from possesses extra
degrees of freedom in terms of the dilaton Φ and the tensor field B.
- The full action contains the
bulk terms in addition to the
- DBI Lagrangian
|
27
|
|
28
|
- It is convenient to write
everything in Einstein's frame using the transformation
|
29
|
- The two parts of the
energy–momentum tensor
- are not in the form of a
perfect fluid. To define r and
p, we make the decomposition
- Πμν is a traceless anisotropic
stress orthogonal to uμuν
- and hμν .
Hence
|
30
|
- A convenient choice is the temporal (synchronous) gauge
- First-order perturbations
- Homogeneity and isotropy imply
- Hence, Φ,i , θ,i and
(Bμν )2 count as first
order
|
31
|
|
32
|
- Retaining only the dominant
terms, the dilaton perturbation satisfies
- with the solution in k-space
- Then, once the perturbations
enter the causal horizon dc (but are still outside the acoustic
horizon ds ), δΦ undergoes rapid damped oscillations,
so that the nonadiabatic perturbation associated with Φ is
destroyed. This means that the nonadiabatic perturbations are not
automatically preserved except at long,
i.e., superhorizon, wavelengths where the simple Chaplygin gas
has no problem anyway.
|
33
|
- The temporal gauge ansatz
|
34
|
|
35
|
|
36
|
|
37
|
- We have achieved the
cancellation of nonadiabatic perturbations with the assurance that this
will hold independent of scale until a~1. With vanishing cs2,
the spatial gradient term is absent, and the density contrast satisfies
- with the growing mode solution
- which is our main result: the
growing mode overdensities here do not display the damped oscillations
of the simple Chaplygin gas below ds but grow as dust. We
remark that it matters little that this applies only for δ > 0 since the Zel'dovich
approximation implies that 92% ends up in overdense regions.
|
38
|
- Navedenu procjenu efekata strune treba shvatiti kao početnu
točku u istraživanju nelinearnih efekata u
općerelativističkoj perturbativnoj analizi
uključujući i polja električnog tipa B0i .
- Možemo očekivati da se akustični horizont ponovo javi kod jako
malih skala što bi možda moglo objasniti sredine (cores) konstantne
gustoće opažene u galaksijama u kojima su dominira tamna materijom.
- Dodavanje novih stupnjeva slobode donekle kvari jednostavnost
kvartesencialnog ujedinjenja tamne materije i tamne energije.
- Na poslijetku, model treba suočiti s opažanjima struktura velike
skale i kozmičkog mikrovalnog zračenja.
|
39
|
- The estimate presented here can be taken as a starting point for
investigating questions beyond linear theory, in the complete
general-relativistic perturbation analysis including the electric-type
field B0i .
- One might hope that the acoustic horizon does resurrect at very small
scales to provide the constant density cores seen in galaxies dominated
by dark matter.
- Adding new degrees of freedom to
some extent spoils the simplicity of quartessence unification.
- Ultimately, the model must be confronted with large-scale structure and
the CMB.
|
40
|
- The DBI Lagrangian is invariant under
- the Kalb-Ramond gauge transformations
|
41
|
- Tamna materija
- tlak >0
- Stvara nehomogene nakupine –
strukture
- Javlja se u blizini barionske materije – galaksije i klasteri
- Tamna energija
- tlak<0
- Homogeno raspodjeljena u svemiru – ne stvara strukture
|
42
|
|