HR-egddlmZmZmZmZmZddlmZddlZ ddlm Z ddl m Z ddlmZddlmZddlmZdd lmZmZer dd lmZmZnd Zd Zd dgZddgiZGdd eZGddeeZdS))acoscosinfsinsqrt)NumberN)log)aszarr) HAS_SCIPY)scalar_inv_efuncs)FLRW FlatFLRWMixin) ellipkinchyp2f1c tdNzNo module named 'scipy.special'ModuleNotFoundErrorargskwargss @lib/python3.11/site-packages/astropy/cosmology/flrw/lambdacdm.pyrr!"CDDDc tdrrrs rrrrr LambdaCDM FlatLambdaCDM*scipyceZdZdZdejzddejzdfdddfd ZdZdZ d Z d Z d Z d Z d ZdZdZdZdZdZdZdZdZdZxZS)raKFLRW cosmology with a cosmological constant and curvature. This has no additional attributes beyond those of FLRW. Parameters ---------- H0 : float or scalar quantity-like ['frequency'] Hubble constant at z = 0. If a float, must be in [km/sec/Mpc]. Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Ode0 : float Omega dark energy: density of the cosmological constant in units of the critical density at z=0. Tcmb0 : float or scalar quantity-like ['temperature'], optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : quantity-like ['energy', 'mass'] or array-like, optional Mass of each neutrino species in [eV] (mass-energy equivalency enabled). If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str or None (optional, keyword-only) Name for this cosmological object. meta : mapping or None (optional, keyword-only) Metadata for the cosmology, e.g., a reference. Examples -------- >>> from astropy.cosmology import LambdaCDM >>> cosmo = LambdaCDM(H0=70, Om0=0.3, Ode0=0.7) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) RQ@Nnamemetac 4t|||||||||  |jjdkrYtj|_|j|j|j f|_ |j dkr| dS|j |_ dS|js:tj|_|j|j|j |j|jzf|_ dStj|_|j|j|j |j|j|j|jf|_ dS)N H0Om0Ode0Tcmb0Neffm_nuOb0r%r&r)super__init___Tcmb0valuer lcdm_inv_efunc_norel_inv_efunc_scalar_Om0_Ode0_Ok0_inv_efunc_scalar_args_optimize_flat_norad _elliptic_comoving_distance_z1z2_comoving_distance_z1z2 _massivenulcdm_inv_efunc_nomnu_Ogamma0_Onu0lcdm_inv_efunc _neff_per_nu _nmasslessnu _nu_y_list) selfr)r*r+r,r-r.r/r%r& __class__s rr1zLambdaCDM.__init__Zs)    ;  ! !%6%KD "+/9dj$)*LD 'yA~~))+++++/3/T,,, %6%KD "     * +D ' ' '&7%ED "    !!+D ' ' 'rc|jdkr&|j|_|j|_|j|_dS|jdkr&|j|_|j|_|j |_dS|j |_|j |_|j |_dS)z>Set optimizations for flat LCDM cosmologies with no radiation.rr N) r6_dS_comoving_distance_z1z2r<_dS_age_age_dS_lookback_time_lookback_time_EdS_comoving_distance_z1z2_EdS_age_EdS_lookback_time&_hypergeometric_comoving_distance_z1z2 _flat_age_flat_lookback_time)rEs rr:zLambdaCDM._optimize_flat_norads 9>>+/+JD ( DI"&"8D    Y!^^+/+KD ( DI"&"9D   +/+VD (DI"&":D   rc|t|}dt|drtj|jndzS)aReturns dark energy equation of state at redshift ``z``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- w : ndarray or float The dark energy equation of state. Returns `float` if the input is scalar. Notes ----- The dark energy equation of state is defined as :math:`w(z) = P(z)/\rho(z)`, where :math:`P(z)` is the pressure at redshift z and :math:`\rho(z)` is the density at redshift z, both in units where c=1. Here this is :math:`w(z) = -1`. gshape?r hasattrnponesrTrEzs rwz LambdaCDM.ws:* 1II71g+>+>Grwqw'''CHHrcvt|}t|drtj|jndS)a*Evaluates the redshift dependence of the dark energy density. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- I : ndarray or float The scaling of the energy density of dark energy with redshift. Returns `float` if the input is scalar. Notes ----- The scaling factor, I, is defined by :math:`\rho(z) = \rho_0 I`, and in this case is given by :math:`I = 1`. rTrUrVrZs rde_density_scalezLambdaCDM.de_density_scales5& 1II#*1g#6#6?rwqwC?rcj tj||\}}n"#t$r}td|d}~wwxYw|jdks|jdks |jdkr|||Sd|jdzz|jz|jdzz }|t|z }|dksd|krd}t||dz zt||dz zzd }d ||d|z zzzdz }t|d|zdzz} dt| z } d| z|dd|zzzzd | zz } ||j|j||| |} ||j|j||| |} nd|kr|dkr|j|jkrd }ttd|z dz }tdttd|z dz z}d d |z|zz}d d d|zz z}d d |z|z z}dt||z z } ||z ||z z } ||j|j|||} ||j|j|||} n|||S|j tt|jz }|| zt| | t| | z zS) aComoving transverse distance in Mpc between two redshifts. This value is the transverse comoving distance at redshift ``z`` corresponding to an angular separation of 1 radian. This is the same as the comoving distance if :math:`\Omega_k` is zero. For :math:`\Omega_{rad} = 0` the comoving distance can be directly calculated as an elliptic integral [1]_. Not valid or appropriate for flat cosmologies (Ok0=0). Parameters ---------- z1, z2 : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshifts. Returns ------- d : `~astropy.units.Quantity` ['length'] Comoving distance in Mpc between each input redshift. References ---------- .. [1] Kantowski, R., Kao, J., & Thomas, R. (2000). Distance-Redshift in Inhomogeneous FLRW. arXiv e-prints, astro-ph/0002334. z1 and z2 have different shapesNrg+ctj|dz|zt|z ||zz|z |dz|zt|z ||zz|zz SNrU)rXarccosabs)r*Ok0kappay1Ar[s rphi_zz9LambdaCDM._elliptic_comoving_distance_z1z2..phi_zsdy#g_s3xx/%"*BDrr UUUUUU?c tjtj||z |dz|zt|z |zz Srd)rXarcsinrrf)r*rgriy2r[s rrkz9LambdaCDM._elliptic_comoving_distance_z1z2..phi_z s>y"r'q3w#oC6PSU6U)V!W!WXXXr)rXbroadcast_arrays ValueErrorr6r7r8 _integral_comoving_distance_z1z2rfpowrrrr_hubble_distancer)rEz1z2ebrhrkv_krirjgk2phi_z1phi_z2ybycrqy3 prefactors rr;z*LambdaCDM._elliptic_comoving_distance_z1z2s6 G(R00FB G G G>??Q F G 9>>TZ1__ Q88R@@ @ $)Q, & 3dil BCFF  EEq1uu    eq1uoQ!a%[(9(997CCCua#g ..!3BR1r6A:&''ADGG Aa%%1q2v:..1q59BU49diArBBFU49diArBBFF!ee!a%%TY%;%; Y Y YT!a%[[1_%%Ba3tAE{{Q///Bb2gl+Bb1r6k*Bb2gl+BDbMM!Ar'b2g&BU49diR<??Q F G$R00rc tj||\}}n"#t$r}td|d}~wwxYwd|jz}||dzdz|dzdzz zS)a Comoving line-of-sight distance in Mpc between objects at redshifts ``z1`` and ``z2`` in a flat, :math:`\Omega_M=1` cosmology (Einstein - de Sitter). The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow. For :math:`\Omega_M=1`, :math:`\Omega_{rad}=0` the comoving distance has an analytic solution. Parameters ---------- z1, z2 : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` ['length'] Comoving distance in Mpc between each input redshift. r`NrarUr)rErwrxryrs rrMz%LambdaCDM._EdS_comoving_distance_z1z2:s, G(R00FB G G G>??Q F G-- R#X84Sh7OOPPrc` tj||\}}n"#t$r}td|d}~wwxYwd|jz |jz dz}|jtj||jzz }||||dzz |||dzz z zS)a Comoving line-of-sight distance in Mpc between objects at redshifts ``z1`` and ``z2``. The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow. For :math:`\Omega_{rad} = 0` the comoving distance can be directly calculated as a hypergeometric function [1]_. Parameters ---------- z1, z2 : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshifts. Returns ------- d : `~astropy.units.Quantity` ['length'] Comoving distance in Mpc between each input redshift. References ---------- .. [1] Baes, M., Camps, P., & Van De Putte, D. (2017). Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology. MNRAS, 468(1), 927-930. r`Nr rlrU)rXrrrsr6rvr_T_hypergeometric)rErwrxrysrs rrPz0LambdaCDM._hypergeometric_comoving_distance_z1z2Xs6 G(R00FB G G G>??Q F G$)mty (g 6)BGA M,B,BB   " "1S> 2 2$$Q"s(^44 5  rc^dtj|ztddd|dz zS)aCompute value using Gauss Hypergeometric function 2F1. .. math:: T(x) = 2 \sqrt(x) _{2}F_{1}\left(\frac{1}{6}, \frac{1}{2}; \frac{7}{6}; -x^3 \right) Notes ----- The :func:`scipy.special.hyp2f1` code already implements the hypergeometric transformation suggested by Baes et al. [1]_ for use in actual numerical evaulations. References ---------- .. [1] Baes, M., Camps, P., & Van De Putte, D. (2017). Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology. MNRAS, 468(1), 927-930. ragUUUUUU?g?g?rb)rXrr)rExs rrzLambdaCDM._T_hypergeometrics/(271::~wAqD' J JJJrct|trtn tj|tt }|j|zS)aAge of the universe in Gyr at redshift ``z``. The age of a de Sitter Universe is infinite. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] The age of the universe in Gyr at each input redshift. )dtype) isinstancerrrX full_likefloat _hubble_time)rEr[ts rrIzLambdaCDM._dS_ages;a(( OCCbl1c.O.O.O 1$$rcBd|jzt|dzdzzS)Age of the universe in Gyr at redshift ``z``. For :math:`\Omega_{rad} = 0` (:math:`T_{CMB} = 0`; massless neutrinos) the age can be directly calculated as an elliptic integral [1]_. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] The age of the universe in Gyr at each input redshift. References ---------- .. [1] Thomas, R., & Kantowski, R. (2000). Age-redshift relation for standard cosmology. PRD, 62(10), 103507. UUUUUU?rUg)rr rZs rrNzLambdaCDM._EdS_ages&*4,,q CT/JJJrc$d|jztjd|jz z }tjtjd|jz dz dzt |dzdzz }||zjS)rrr yrUrb)rrXemathrr6arcsinhr real)rEr[rargs rrQzLambdaCDM._flat_ages. 11BHMM!di-4P4PP j HMM1ty=1,r1fQii#o!5KK L L  C%%rcX|d||z S)aLookback time in Gyr to redshift ``z``. The lookback time is the difference between the age of the Universe now and the age at redshift ``z``. For :math:`\Omega_{rad} = 0` (:math:`T_{CMB} = 0`; massless neutrinos) the age can be directly calculated as an elliptic integral. The lookback time is here calculated based on the ``age(0) - age(z)``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] Lookback time in Gyr to each input redshift. r)rNrZs rrOzLambdaCDM._EdS_lookback_times'(}}Q$--"2"222rcP|jtt|dzzS)aLookback time in Gyr to redshift ``z``. The lookback time is the difference between the age of the Universe now and the age at redshift ``z``. For :math:`\Omega_{rad} = 0` (:math:`T_{CMB} = 0`; massless neutrinos) the age can be directly calculated. .. math:: a = exp(H * t) \ \text{where t=0 at z=0} t = (1/H) (ln 1 - ln a) = (1/H) (0 - ln (1/(1+z))) = (1/H) ln(1+z) Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] Lookback time in Gyr to each input redshift. rU)rr r rZs rrKzLambdaCDM._dS_lookback_times$2 3vayy3#7#777rcX|d||z S)aLookback time in Gyr to redshift ``z``. The lookback time is the difference between the age of the Universe now and the age at redshift ``z``. For :math:`\Omega_{rad} = 0` (:math:`T_{CMB} = 0`; massless neutrinos) the age can be directly calculated. The lookback time is here calculated based on the ``age(0) - age(z)``. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- t : `~astropy.units.Quantity` ['time'] Lookback time in Gyr to each input redshift. r)rQrZs rrRzLambdaCDM._flat_lookback_time s'(~~a  4>>!#4#444rc|j|js|jn|j||zz}t |dz}t j|dz||z|jz|z|jzz|j zS)Function used to calculate H(z), the Hubble parameter. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- E : ndarray or float The redshift scaling of the Hubble constant. Returns `float` if the input is scalar. Defined such that :math:`H(z) = H_0 E(z)`. rUra) r?r=r@nu_relative_densityr rXrr6r8r7rEr[Orzp1s refunczLambdaCDM.efunc#s"]? =DJJ!9!9!! ?$* L   rc|j|js|jn|j||zz}t |dz}|dz||z|jz|z|jzz|jzdzS)Function used to calculate :math:`\frac{1}{H_z}`. Parameters ---------- z : Quantity-like ['redshift'], array-like, or `~numbers.Number` Input redshift. Returns ------- E : ndarray or float The inverse redshift scaling of the Hubble constant. Returns `float` if the input is scalar. Defined such that :math:`H_z = H_0 / E`. rUrar)r?r=r@rr r6r8r7rs r inv_efunczLambdaCDM.inv_efunc?s]? =DJJ!9!9!!>> from astropy.cosmology import FlatLambdaCDM >>> cosmo = FlatLambdaCDM(H0=70, Om0=0.3) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) To get an equivalent cosmology, but of type `astropy.cosmology.LambdaCDM`, use :attr:`astropy.cosmology.FlatFLRWMixin.nonflat`. >>> cosmo.nonflat LambdaCDM(H0=70.0 km / (Mpc s), Om0=0.3, ... r"r#Nr$c t||d|||||| |jjdkr:tj|_|j|jf|_ | dS|j s4tj |_|j|j|j |jzf|_ dStj|_|j|j|j |j|j|jf|_ dS)Nr"r(r)r0r1r2r3r flcdm_inv_efunc_norelr5r6r7r9r:r=flcdm_inv_efunc_nomnur?r@flcdm_inv_efuncrBrCrD) rEr)r*r,r-r.r/r%r&rFs rr1zFlatLambdaCDM.__init__s    ;  ! !%6%LD "+/9dj*AD '  % % ' ' ' ' ' %6%LD "    *+D ' ' ' &7%FD "   !! +D ' ' 'rc|j|js|jn|j||zz}t |dz}t j|dz||z|jzz|jzS)rrUrb) r?r=r@rr rXrr6r7rs rrzFlatLambdaCDM.efuncst"]? =DJJ!9!9!!rs+*******************888888%%%%%%%% E/////////EEEEEE  (gY'v v v v v v v v r]H]H]H]H]HM9]H]H]H]H]Hr