As far as I know there are nine types of sex in Hinduism. A man cannot touch his wife immediately after marriage.
Question: How many days after marriage can a man touch his wife?
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Definitely not on the First Night of marriage.
Why not ?
Naandi-shraddham (which is pitru-karyam) is one of the main Vedic rituals done on day of marriage.
So what ?
On days of pitru-karyam days like amavasya and shraddha, cohabitation is prohibited.
LXXIX. — Sixteen nights are the season of women. Among these he should approach them during the even nights. Let him avoid the Parvana nights and the first four nights
Parvana includes Amavasya and Shraddha days. On day of marriage, Shraddha is done. Hence it is Parvana. Hence to be avoided.
Next, not for 5 days after marriage, because brahmacharya vratham has to be maintained.
Vedic scholars at Veda Patashala.
Next, not until after the wife has had her first menstruation.
Why not ?
The day of marriage is fixed so that it does not occur during the bride's periods. So it has to fall somewhere in the 24 days between her period end and period start. Out of these, only 12 are allowed for cohabitation (source above : 16 minus 4). If marriage is fixed on 1st day, then after 5 days of brahmacharya vrat, it is still in allowed time-period, so no problem. But the chances of this happening are low, as marriage date will statistically fall in middle on 6th day. And after 5-days brahmacharya vrat rule, the 12 allowable days would be over. Hence, wait until the first menstrual period comes and goes, which will happen within a couple of weeks
Next, for those who maintain agnihotra (vaidika brahmanas), 6 months of brahmacharyam is stipulated.
Vedic scholars at Veda Patashala.
For most normal folks, it is a test of both your mental strength and obedience to shastras, to wait for about 1 month after marriage.
Even otherwise, during that initial month, the new couple visit temples, relatives and elders etc. to get blessings, socialize, introduce wife to her new family, and to remind them that marriage has a higher goal of following dharma, and that kama is subservient to that. And it takes some time for husband and wife to get comfortable with each other, at least in arranged marriages.
It is not recommended to have shanthi-muhurtam outside the house in some hotel. The wedding-bed is a present made specifically for that and special days are stipulated for the night. The use of contraception is also a modern-day concept alien to shastras, so natural fertility cycle can be taken into account if progeny is not in the plans immediately. They can go on honey-moon after above ritual is completed at home.
The underlying theme is not to rely on physical contact for intimacy to grow between the couple, but that as long as both have a common goal higher than themselves, mental intimacy will grow, and physical union will help in that goal.
TL:DR; Avoid sex on marriage day (First Night) because it is holy day for pitrus (ancestors). Wait for ~1 month, or until after wife's first menses is over.
According to the Kamasutra of Vatsyayana, husbands are advised to abstain from any sexual contact for the first nine days. It is only on the tenth day that the husband is advised to "create confidence" in his wife:
For the first three days after marriage, the girl and her husband should sleep on the floor, abstain from sexual pleasures, and eat their food without seasoning it either with alkali or salt. For the next seven days they should bathe amidst tire sounds of auspicious musical instruments, should decorate themselves, dine together, and pay attention to their relations as well as to those who may have come to witness their marriage. This is applicable to persons of all castes. On the night of the tenth day the man should begin in a lonely place with soft words, and thus create confidence in the girl. Some authors say that for the purpose of winning her over he should not speak to her for three days, but the followers of Babhravya are of opinion that if the man does not speak with her for three days, the girl may be discouraged by seeing him spiritless like a pillar, and, becoming dejected, she may begin to despise him as a eunuch. Vatsyayana says that the man should begin to win her over, and to create confidence in her, but should abstain at first from sexual pleasures. Women, being of a tender nature, want tender beginnings, and when they are forcibly approached by men with whom they are but slightly acquainted, they sometimes suddenly become haters of sexual connection, and sometimes even haters of the male sex. The man should therefore approach the girl according to her liking, and should make use of those devices by which he may be able to establish himself more and more into her confidence. (Kamasutra of Vatsyayana, Chapter 17)